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Generic properties of invariant measures of full-shift systems over perfect Polish metric spaces Stoch. Dyn. (IF 0.742) Pub Date : 2021-01-09 Silas L. Carvalho; Alexander Condori
In this work, we are interested in characterizing typical (generic) dimensional properties of invariant measures associated with the full-shift system, T, in a product space whose alphabet is a perfect Polish metric space (thus, uncountable). More specifically, we show that the set of invariant measures with upper Hausdorff dimension equal to zero and lower packing dimension equal to infinity is a
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On the liftability of expanding stationary measures Stoch. Dyn. (IF 0.742) Pub Date : 2021-01-07 José F. Alves; Carla L. Dias; Helder Vilarinho
We consider random perturbations of a topologically transitive local diffeomorphism of a Riemannian manifold. We show that if an absolutely continuous ergodic stationary measures is expanding (all Lyapunov exponents positive), then there is a random Gibbs–Markov–Young structure which can be used to lift that measure. We also prove that if the original map admits a finite number of expanding invariant
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On some properties of sticky Brownian motion Stoch. Dyn. (IF 0.742) Pub Date : 2020-12-14 Haoyan Zhang; Pingping Jiang
In this paper, we investigate a generalization of Brownian motion, called sticky skew Brownian motion, which has two interesting characteristics: stickiness and skewness. This kind of processes spends a lot more time at its sticky points so that the time they spend at the sticky points has positive Lebesgue measure. By using time change, we obtain an SDE for the sticky skew Brownian motion. Then, we
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Boundary entropy spectra as finite subsums Stoch. Dyn. (IF 0.742) Pub Date : 2020-12-14 Hanna Oppelmayer
In this paper, we provide a concrete construction of Furstenberg entropy values of τ-boundaries of the group ℤ[1p1,…,1pl]⋊{p1n1⋯plnl:ni∈ℤ} by choosing an appropriate random walk τ. We show that the boundary entropy spectrum can be realized as the subsum-set for any given finite sequence of positive numbers.
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Mean-field backward–forward stochastic differential equations and nonzero sum stochastic differential games Stoch. Dyn. (IF 0.742) Pub Date : 2020-12-03 Yinggu Chen; Boualem Djehiche; Said Hamadène
We study a general class of fully coupled backward–forward stochastic differential equations of mean-field type (MF-BFSDE). We derive existence and uniqueness results for such a system under weak monotonicity assumptions and without the non-degeneracy condition on the forward equation. This is achieved by suggesting an implicit approximation scheme that is shown to converge to the solution of the system
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Predictive sets Stoch. Dyn. (IF 0.742) Pub Date : 2020-11-25 Nishant Chandgotia; Benjamin Weiss
A set P⊂ℕ is called predictive if for any zero entropy finite-valued stationary process (Xi)i∈ℤ, X0 is measurable with respect to (X−i)i∈P. We know that ℕ is a predictive set. In this paper, we give sufficient conditions and necessary ones for a set to be predictive. We also discuss linear predictivity, predictivity among Gaussian processes and relate these to Riesz sets which arise in harmonic analysis
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Unique equilibrium states for some intermediate beta transformations Stoch. Dyn. (IF 0.742) Pub Date : 2020-11-25 Leonard Carapezza; Marco López; Donald Robertson
We prove uniqueness of equilibrium states for subshifts corresponding to intermediate beta transformations with β>2 having the property that the orbit of 0 is bounded away from 1.
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Almost periodicity and periodicity for nonautonomous random dynamical systems Stoch. Dyn. (IF 0.742) Pub Date : 2020-11-23 Paul Raynaud de Fitte
We present a notion of almost periodicity which can be applied to random dynamical systems as well as almost periodic stochastic differential equations in Hilbert spaces (abstract stochastic partial differential equations). This concept allows for improvements of known results of almost periodicity in distribution, for general random processes and for solutions to stochastic differential equations
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Wong–Zakai approximations and attractors for stochastic degenerate parabolic equations on unbounded domains Stoch. Dyn. (IF 0.742) Pub Date : 2020-11-12 Fahe Miao; Hui Liu; Jie Xin
The Wong–Zakai approximations given by a stationary process and attractors for stochastic degenerate parabolic equations are considered in this paper. We first establish the existence and uniqueness of tempered pullback attractors for the Wong–Zakai approximations of stochastic degenerate parabolic equations. We then prove that the attractors of Wong–Zakai approximations converge to the attractor of
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A result on the Laplace transform associated with the sticky Brownian motion on an interval Stoch. Dyn. (IF 0.742) Pub Date : 2020-10-28 Shiyu Song
In this paper, we study the joint Laplace transform of the sticky Brownian motion on an interval, its occupation time at zero and its integrated process. The perturbation approach of Li and Zhou [The joint Laplace transforms for diffusion occupation times, Adv. Appl. Probab.45 (2013) 1049–1067] is adopted to convert the problem into the computation of three Laplace transforms, which is essentially
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General fully coupled FBSDES involving the value function and related nonlocal HJB equations combined with algebraic equations Stoch. Dyn. (IF 0.742) Pub Date : 2020-10-24 Tao Hao; Qingfeng Zhu
Recently, Hao and Li [Fully coupled forward-backward SDEs involving the value function. Nonlocal Hamilton–Jacobi–Bellman equations, ESAIM: Control Optim, Calc. Var.22(2016) 519–538] studied a new kind of forward-backward stochastic differential equations (FBSDEs), namely the fully coupled FBSDEs involving the value function in the case where the diffusion coefficient σ in forward stochastic differential
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Typical dynamics and fluctuation analysis of slow–fast systems driven by fractional Brownian motion Stoch. Dyn. (IF 0.742) Pub Date : 2020-10-13 Solesne Bourguin; Siragan Gailus; Konstantinos Spiliopoulos
This paper studies typical dynamics and fluctuations for a slow–fast dynamical system perturbed by a small fractional Brownian noise. Based on an ergodic theorem with explicit rates of convergence, which may be of independent interest, we characterize the asymptotic dynamics of the slow component to two orders (i.e. the typical dynamics and the fluctuations). The limiting distribution of the fluctuations
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The identification problem for BSDEs driven by possibly non-quasi-left-continuous random measures Stoch. Dyn. (IF 0.742) Pub Date : 2020-09-17 Elena Bandini; Francesco Russo
In this paper, we focus on the so-called identification problem for a BSDE driven by a continuous local martingale and a possibly non-quasi-left-continuous random measure. Supposing that a solution (Y,Z,U) of a BSDE is such that Yt=v(t,Xt), where X is an underlying process and v is a deterministic function, solving the identification problem consists in determining Z and U in terms of v. We study the
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Global solution of nonlinear stochastic heat equation with solutions in a Hilbert manifold Stoch. Dyn. (IF 0.742) Pub Date : 2020-09-17 Zdzisław Brzeźniak; Javed Hussain
The objective of this paper is to prove the existence of a global solution to a certain stochastic partial differential equation subject to the L2-norm being constrained. The corresponding evolution equation can be seen as the projection of the unconstrained problem onto the tangent space of the unit sphere ℳ in a Hilbert space L2.
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Renormalized Onsager functions and merging of vortex clusters Stoch. Dyn. (IF 0.742) Pub Date : 2020-08-28 Franco Flandoli
This paper is devoted to an heuristic discussion of the merging mechanism between two clusters of point vortices, supported by some numerical simulations. A concept of renormalized Onsager function is introduced, elaboration of the solutions of the mean field equation. It is used to understand the shape of the single cluster observed as a result of the merging process. Potential implications for the
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Synchronization by noise for the stochastic quantization equation in dimensions 2 and 3 Stoch. Dyn. (IF 0.742) Pub Date : 2020-09-19 Benjamin Gess; Pavlos Tsatsoulis
We prove uniform synchronization by noise with rates for the stochastic quantization equation in dimensions two and three. The proof relies on a combination of coming down from infinity estimates and the framework of order-preserving Markov semigroups derived in [O. Butkovsky and M. Scheutzow, Couplings via comparison principle and exponential ergodicity of SPDEs in the hypoelliptic setting, preprint
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Decay of correlation rate in the mean field limit of point vortices ensembles Stoch. Dyn. (IF 0.742) Pub Date : 2020-08-18 Francesco Grotto; Marco Romito
We consider the Mean Field limit of Gibbsian ensembles of 2-dimensional (2D) point vortices on the torus. It is a classical result that in such limit correlations functions converge to 1, that is, point vortices decorrelate: We compute the rate at which this convergence takes place by means of Gaussian integration techniques, inspired by the correspondence between the 2D Coulomb gas and the Sine-Gordon
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Spatial dynamics in interacting systems with discontinuous coefficients and their continuum limits Stoch. Dyn. (IF 0.742) Pub Date : 2020-08-28 Giovanni Zanco
We consider a discrete model in which particles are characterized by two quantities X and Y; both quantities evolve in time according to stochastic dynamics and the equation that governs the evolution of Y is also influenced by mean-field interaction between the particles. We allow for discontinuous coefficients and random initial condition and, under suitable assumptions, we prove that in the limit
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Well-posedness of SVI solutions to singular-degenerate stochastic porous media equations arising in self-organized criticality Stoch. Dyn. (IF 0.742) Pub Date : 2020-09-30 Marius Neuss
We consider a class of generalized stochastic porous media equations with multiplicative Lipschitz continuous noise. These equations can be related to physical models exhibiting self-organized criticality. We show that these SPDEs have unique SVI solutions which depend continuously on the initial value. In order to formulate this notion of solution and to prove uniqueness in the case of a slowly growing
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Synchronization by noise for the stochastic quantization equation in dimensions 2 and 3 Stoch. Dyn. (IF 0.742) Pub Date : 2020-09-19 Benjamin Gess; Pavlos Tsatsoulis
We prove uniform synchronization by noise with rates for the stochastic quantization equation in dimensions two and three. The proof relies on a combination of coming down from infinity estimates and the framework of order-preserving Markov semigroups derived in [O. Butkovsky and M. Scheutzow, Couplings via comparison principle and exponential ergodicity of SPDEs in the hypoelliptic setting, preprint
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On generalized compensation functions for factor maps between shift spaces on countable alphabets Stoch. Dyn. (IF 0.742) Pub Date : 2020-09-19 Camilo Lacalle; Yuki Yayama
We show the existence of generalized compensation functions for a particular type of one-block factor maps π:X→Y between countable subshifts X and Y. For factor maps between compact spaces, continuous compensation functions were studied by Walters in relation to the theory of relative pressure. Applying the thermodynamic formalism for sequences on countable subshifts, we generalize some existing results
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Cramér-type moderate deviations for the likelihood ratio process of Ornstein–Uhlenbeck process with shift Stoch. Dyn. (IF 0.742) Pub Date : 2020-09-17 Hui Jiang; Hui Liu
For the Ornstein–Uhlenbeck process in stationary and explosive cases, this paper studies Cramér-type moderate deviations for the log-likelihood ratio process. As an application, we give the negative regions of drift testing problem, and also obtain the decay rates of the error probabilities. The main methods of this paper consist of mod-ϕ convergence approach, deviation inequalities for multiple Wiener–Itô
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Some characterizations for the CIR model with Markov switching Stoch. Dyn. (IF 0.742) Pub Date : 2020-09-09 Jinying Tong; Yaqin Sun; Zhenzhong Zhang; Tiandao Zhou; Zhenjiang Qin
Recently, the Cox–Ingersoll–Ross (CIR) model with Markov switching has been discussed extensively. However, the covariance function and the kth moment for this model are still open. In this paper, we consider some characterizations for the CIR model with Markov switching. First, the conditional moment generating functions for CIR model with Markov switching are given. Then, explicit expressions for
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Higher order asymptotics for large deviations — Part II Stoch. Dyn. (IF 0.742) Pub Date : 2020-09-09 Kasun Fernando; Pratima Hebbar
We obtain asymptotic expansions for the large deviation principle (LDP) for continuous time stochastic processes with weakly-dependent increments. As a key example, we show that additive functionals of solutions of stochastic differential equations (SDEs) satisfying Hörmander condition on a d-dimensional compact manifold admit these asymptotic expansions of all orders.
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Large deviation for two-time-scale stochastic burgers equation Stoch. Dyn. (IF 0.742) Pub Date : 2020-09-05 Xiaobin Sun; Ran Wang; Lihu Xu; Xue Yang
A Freidlin–Wentzell type large deviation principle is established for stochastic partial differential equations with slow and fast time-scales, where the slow component is a one-dimensional stochastic Burgers equation with small noise and the fast component is a stochastic reaction-diffusion equation. Our approach is via the weak convergence criterion developed in [A. Budhiraja and P. Dupuis, A variational
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A non-conservation stochastic partial differential equation driven by anisotropic fractional Lévy random field Stoch. Dyn. (IF 0.742) Pub Date : 2020-09-05 Xuebin Lü; Wanyang Dai
We study a non-conservation second-order stochastic partial differential equation (SPDE) driven by multi-parameter anisotropic fractional Lévy noise (AFLN) and under different initial and/or boundary conditions. It includes the time-dependent linear heat equation and quasi-linear heat equation under the fractional noise as special cases. Unique existence and expressions of solution to the equation
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Necessary and sufficient condition for ℳ2-convergence to a Lévy process for billiards with cusps at flat points Stoch. Dyn. (IF 0.742) Pub Date : 2020-09-04 Paul Jung; Ian Melbourne; Françoise Pène; Paulo Varandas; Hong-Kun Zhang
We consider a class of planar dispersing billiards with a cusp at a point of vanishing curvature. Convergence to a stable law and to the corresponding Lévy process in the ℳ1 and ℳ2 Skorohod topologies has been studied in recent work. Here, we show that certain sufficient conditions for ℳ2-convergence are also necessary.
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On the spectral radius of compact operator cocycles Stoch. Dyn. (IF 0.742) Pub Date : 2020-09-04 Lucas Backes; Davor Dragičević
We extend the notions of joint and generalized spectral radii to cocycles acting on Banach spaces and obtain a version of Berger–Wang’s formula when restricted to the space of cocycles taking values in the space of compact operators. Moreover, we observe that the previous quantities depends continuously on the underlying cocycle.
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Unstable entropy and unstable pressure for random partially hyperbolic dynamical systems Stoch. Dyn. (IF 0.742) Pub Date : 2020-09-03 Xinsheng Wang; Weisheng Wu; Yujun Zhu
Let ℱ be a C2 random partially hyperbolic dynamical system. For the unstable foliation, the corresponding unstable metric entropy, unstable topological entropy and unstable pressure via the dynamics of ℱ on the unstable foliation are introduced and investigated. A version of Shannon–McMillan–Breiman Theorem for unstable metric entropy is given, and a variational principle for unstable pressure (and
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Numerical resonances for Schottky surfaces via Lagrange–Chebyshev approximation Stoch. Dyn. (IF 0.742) Pub Date : 2020-08-28 Oscar F. Bandtlow; Anke Pohl; Torben Schick; Alexander Weiße
We present a numerical method to calculate resonances of Schottky surfaces based on Selberg theory, transfer operator techniques and Lagrange–Chebyshev approximation. This method is an alternative to the method based on periodic orbit expansion used previously in this context.
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Mean exit time and escape probability for the stochastic logistic growth model with multiplicative α-stable Lévy noise Stoch. Dyn. (IF 0.742) Pub Date : 2020-08-28 Almaz Tesfay; Daniel Tesfay; Anas Khalaf; James Brannan
In this paper, we formulate a stochastic logistic fish growth model driven by both white noise and non-Gaussian noise. We focus our study on the mean time to extinction, escape probability to measure the noise-induced extinction probability and the Fokker–Planck equation for fish population X(t). In the Gaussian case, these quantities satisfy local partial differential equations while in the non-Gaussian
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The Kramers problem for SDEs driven by small, accelerated Lévy noise with exponentially light jumps Stoch. Dyn. (IF 0.742) Pub Date : 2020-08-28 André de Oliveira Gomes; Michael A. Högele
We establish Freidlin–Wentzell results for a nonlinear ordinary differential equation starting close to the stable state 0, say, subject to a perturbation by a stochastic integral which is driven by an 𝜀-small and (1/𝜀)-accelerated Lévy process with exponentially light jumps. For this purpose, we derive a large deviations principle for the stochastically perturbed system using the weak convergence
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On a question of H. A. Schwarz Stoch. Dyn. (IF 0.742) Pub Date : 2020-08-21 S. J. Patterson
This work described here is part of a project to document the life and work of Kurt Heegner (1893–1965) whose papers have been deposited in the Handschriftenabteilung of the SUB Göttingen. The question with which this paper is concerned is the rationality of the variety which describes the connection of the volume of a tetrahedron with its side-lengths (Cayley–Menger formula).
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Uniform attractors for a class of stochastic evolution equations with multiplicative fractional noise Stoch. Dyn. (IF 0.742) Pub Date : 2020-08-21 Caibin Zeng; Xiaofang Lin; Hongyong Cui
This paper studies the (random) uniform attractor for a class of non-autonomous stochastic evolution equations driven by a time-periodic forcing and multiplicative fractional noise with Hurst parameter bigger than 1/2. We first establish the existence and uniqueness results for the solution to the considered equation and show that the solution generates a jointly continuous non-autonomous random dynamical
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Existence of densities for stochastic evolution equations driven by fractional Brownian motion Stoch. Dyn. (IF 0.742) Pub Date : 2020-08-21 Jorge A. de Nascimento; Alberto Ohashi
In this work, we prove a version of Hörmander’s theorem for a stochastic evolution equation driven by a trace-class fractional Brownian motion with Hurst exponent 12
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On the macroscopic limit of Brownian particles with local interaction Stoch. Dyn. (IF 0.742) Pub Date : 2020-08-05 Franco Flandoli; Marta Leocata; Cristiano Ricci
An interacting particle system made of diffusion processes with local interaction is considered and the macroscopic limit to a nonlinear PDE is investigated. Few rigorous results exists on this problem and in particular the explicit form of the nonlinearity is not known. This paper reviews this subject, some of the main ideas to get the limit nonlinear PDE and provides both heuristic and numerical
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On the macroscopic limit of Brownian particles with local interaction Stoch. Dyn. (IF 0.742) Pub Date : 2020-08-05 Franco Flandoli; Marta Leocata; Cristiano Ricci
An interacting particle system made of diffusion processes with local interaction is considered and the macroscopic limit to a nonlinear PDE is investigated. Few rigorous results exists on this problem and in particular the explicit form of the nonlinearity is not known. This paper reviews this subject, some of the main ideas to get the limit nonlinear PDE and provides both heuristic and numerical
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Maximum likelihood estimation for symmetric α-stable Ornstein–Uhlenbeck processes Stoch. Dyn. (IF 0.742) Pub Date : 2020-07-30 Zhifen Chen; Xiaopeng Chen
In this paper, we consider the maximum likelihood estimation for the symmetric α-stable Ornstein–Uhlenbeck (SαS-OU) processes based on discrete observations. Since the closed-form expression of maximum likelihood function is hard to obtain in the Lévy case, we choose a mixture of Cauchy and Gaussian distribution to approximate the probability density function (PDF) of the SαS distribution. By means
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Attractors for 2D quasi-geostrophic equations with and without colored noise in W2α−,p(ℝ2) Stoch. Dyn. (IF 0.742) Pub Date : 2020-07-25 Lin Yang; Yejuan Wang
The asymptotic behavior of stochastic modified quasi-geostrophic equations with damping driven by colored noise is analyzed. In fact, the existence of random attractors is established in W2α−,p(ℝ2). In particular, we prove also the existence of a global compact attractor for autonomous quasi-geostrophic equations with damping in W2α−,p(ℝ2). Here, we do not add any modifying factor on the nonlinear
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On the existence of a σ-finite acim for a random iteration of intermittent Markov maps with uniformly contractive part Stoch. Dyn. (IF 0.742) Pub Date : 2020-07-20 Hisayoshi Toyokawa
For an annealed type random dynamical system arising from non-uniformly expanding maps which admits uniformly contractive branches, we establish the existence of an absolutely continuous σ-finite invariant measure. We also show when the invariant measure is infinite.
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Quantum Feller semigroup in terms of quantum Bernoulli noises Stoch. Dyn. (IF 0.742) Pub Date : 2020-06-18 Jinshu Chen
Quantum Bernoulli noises (QBN) are the family of annihilation and creation operators acting on Bernoulli functionals, which satisfy a canonical anti-commutation relation in equal-time. In this paper, we aim to investigate quantum Feller semigroups in terms of QBN. We first investigate local structure of the algebra generated by identity operator and QBN. We then use our new results obtained here to
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Averaging principle for impulsive stochastic partial differential equations Stoch. Dyn. (IF 0.742) Pub Date : 2020-06-15 Jiankang Liu; Wei Xu; Qin Guo
This paper focuses on systems of stochastic partial differential equations with impulse effects. We establish an averaging principle such that the solution to the complex original nonlinear impulsive stochastic evolution equations can be approximated by that to the more simplified averaged stochastic evolution equations without impulses. By adopting stochastic analysis theory, semigroup approach and
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Hyperviscous stochastic Navier–Stokes equations with white noise invariant measure Stoch. Dyn. (IF 0.742) Pub Date : 2020-06-25 M. Gubinelli; M. Turra
We prove existence and uniqueness of martingale solutions to a (slightly) hyper-viscous stochastic Navier–Stokes equation in 2d with initial conditions absolutely continuous with respect to the Gibbs measure associated to the energy, getting the results both in the torus and in the whole space setting.
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Limit theorems for numbers of returns in arrays under ϕ-mixing Stoch. Dyn. (IF 0.742) Pub Date : 2020-06-18 Yuri Kifer
We consider a ϕ-mixing shift T on a sequence space Ω and study the number 𝒩N of returns {TqN(n)ω∈Ana} at times qN(n) to a cylinder Ana constructed by a sequence a∈Ω where n runs either until a fixed integer N or until a time τN of the first return {TqN(n)ω∈Amb} to another cylinder Amb constructed by b∈Ω. Here, qN(n) are certain functions of n taking on nonnegative integer values when n runs from 0
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Controllability for impulsive neutral stochastic delay partial differential equations driven by fBm and Lévy noise Stoch. Dyn. (IF 0.742) Pub Date : 2020-06-18 Diem Dang Huan; Ravi P. Agarwal
This paper aims to investigate the controllability for impulsive neutral stochastic delay partial differential equations (PDEs) driven by fractional Brownian motion (fBm) with Hurst index H∈(12,1) and Lévy noise in Hilbert spaces. By using a fixed point approach without imposing a severe compactness condition on the semigroup, a new set of sufficient conditions is derived. The results in this paper
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Regularized vortex approximation for 2D Euler equations with transport noise Stoch. Dyn. (IF 0.742) Pub Date : 2020-06-05 Michele Coghi; Mario Maurelli
We study a mean field approximation for the 2D Euler vorticity equation driven by a transport noise. We prove that the Euler equations can be approximated by interacting point vortices driven by a regularized Biot–Savart kernel and the same common noise. The approximation happens by sending the number of particles N to infinity and the regularization 𝜖 in the Biot–Savart kernel to 0, as a suitable
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Weak well-posedness of multidimensional stable driven SDEs in the critical case Stoch. Dyn. (IF 0.742) Pub Date : 2020-06-05 Paul-Éric Chaudru de Raynal; Stéphane Menozzi; Enrico Priola
We establish weak well-posedness for critical symmetric stable driven SDEs in ℝd with additive noise Z, d≥1. Namely, we study the case where the stable index of the driving process Z is α=1 which exactly corresponds to the order of the drift term having the coefficient b which is continuous and bounded. In particular, we cover the cylindrical case when Zt=(Zt1,…,Ztd) and Z1,…,Zd are independent one-dimensional
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Randomly switched vector fields sharing a zero on a common invariant face Stoch. Dyn. (IF 0.742) Pub Date : 2020-06-05 Edouard Strickler
We consider a Piecewise Deterministic Markov Process given by random switching between finitely many vector fields vanishing at 0. It has been shown recently that the behavior of this process is mainly determined by the signs of Lyapunov exponents. However, results have only been given when all these exponents have the same sign. In this paper, we consider the degenerate case where the process leaves
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Dynamics of cholera epidemic models in fluctuating environments Stoch. Dyn. (IF 0.742) Pub Date : 2020-06-05 Tuan Anh Phan; Jianjun Paul Tian; Bixiang Wang
Based on our deterministic models for cholera epidemics, we propose a stochastic model for cholera epidemics to incorporate environmental fluctuations which is a nonlinear system of Itô stochastic differential equations. We conduct an asymptotical analysis of dynamical behaviors for the model. The basic stochastic reproduction value ℛs is defined in terms of the basic reproduction number R0 for the
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Fair measures for countable-to-one maps Stoch. Dyn. (IF 0.742) Pub Date : 2020-06-04 Ana Rodrigues; Samuel Roth; Zuzana Roth
In this paper, we generalize the recently introduced concept of fair measure [M. Misiurewicz and A. Rodrigues, Counting preimages, Ergod. Theor. Dyn. Syst. 38 (2018) 1837–1856]. We study fair measures for Markov and mixing interval maps with countably many branches. We investigate them in terms of the recurrence properties of some underlying countable Markov shifts, both from the stochastic viewpoint
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Asymptotic expansion for the quadratic variations of the solution to the heat equation with additive white noise Stoch. Dyn. (IF 0.742) Pub Date : 2020-06-03 Héctor Araya; Ciprian A. Tudor
We consider the sequence of spatial quadratic variations of the solution to the stochastic heat equation with space-time white noise. This sequence satisfies a Central Limit Theorem. By using Malliavin calculus, we refine this result by proving the convergence of the sequence of densities and by finding the second-order term in the asymptotic expansion of the densities. In particular, our proofs are
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Three variations on a theme by Fibonacci Stoch. Dyn. (IF 0.742) Pub Date : 2020-04-14 Michael Baake; Natalie Priebe Frank; Uwe Grimm
Several variants of the classic Fibonacci inflation tiling are considered in an illustrative fashion, in one and in two dimensions, with an eye on changes or robustness of diffraction and dynamical spectra. In one dimension, we consider extension mechanisms of deterministic and of stochastic nature, while we look at direct product variations in a planar extension. For the pure point part, we systematically
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Homeomorphism flows for SDEs driven by G-Brownian motion with non-Lipschitz coefficients Stoch. Dyn. (IF 0.742) Pub Date : 2020-03-19 Juanfang Liu; Yu Miao; Jianyong Mu; Jie Xu
In this paper, we shall prove the homeomorphism property of solutions for multidimensional stochastic differential equations (SDEs) driven by G-Brownian motion with non-Lipschitz coefficients with respect to the initial values.
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Splitting-up scheme for the stochastic Cahn–Hilliard Navier–Stokes model Stoch. Dyn. (IF 0.742) Pub Date : 2020-03-18 Gabriel Deugoue; Boris Jidjou Moghomye; Theodore Tachim Medjo
In this paper, we consider a stochastic Cahn–Hilliard Navier–Stokes system in a bounded domain of ℝd,d=2,3. The system models the evolution of an incompressible isothermal mixture of binary fluids under the influence of stochastic external forces. We prove the existence of a global weak martingale solution. The proof is based on the splitting-up method as well as some compactness method.
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The multi-transitivity of free semigroup actions Stoch. Dyn. (IF 0.742) Pub Date : 2020-03-12 Zhumin Ding; Jiandong Yin; Xiaofang Luo
In this paper, we introduce the conceptions of multi-transitivity, Δ-transitivity and Δ-mixing property for free semigroup actions and give some equivalent conditions for a free semigroup action to be multi-transitive, multi-transitive with respect to vectors and strongly multi-transitive, respectively. For instance, we prove that a free semigroup action is multi-transitive or multi-transitive with
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A scaling limit for the stochastic mSQG equations with multiplicative transport noises Stoch. Dyn. (IF 0.742) Pub Date : 2020-03-11 Dejun Luo; Martin Saal
We consider on the 2D torus the modified Surface Quasi-Geostrophic (mSQG) equation with L2-initial data and perturbed by multiplicative transport noise. Under a suitable scaling of the noises, we show that the solutions converge weakly to the unique solution of the dissipative mSQG equation.
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Approximation of solutions of mean-field stochastic differential equations Stoch. Dyn. (IF 0.742) Pub Date : 2020-03-11 Oussama Elbarrimi; Youssef Ouknine
Our aim in this paper is to establish some strong stability properties of solutions of mean-field stochastic differential equations. These latter are stochastic differential equations where the coefficients depend not only on the state of the unknown process but also on its probability distribution. The results are obtained assuming that the pathwise uniqueness property holds and using Skorokhod’s
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Extended backward stochastic Volterra integral equations, Quasilinear parabolic equations, and Feynman–Kac formula Stoch. Dyn. (IF 0.742) Pub Date : 2020-03-11 Hanxiao Wang
This paper is concerned with the relationship between backward stochastic Volterra integral equations (BSVIEs, for short) and a kind of non-local quasilinear (and possibly degenerate) parabolic equations. As a natural extension of BSVIEs, the extended BSVIEs (EBSVIEs, for short) are introduced and investigated. Under some mild conditions, the well-posedness of EBSVIEs is established and some regularity
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Attractors with higher-order regularity of stochastic reaction–diffusion equations on time-varying domains Stoch. Dyn. (IF 0.742) Pub Date : 2020-03-02 Lu Yang; Meihua Yang; Peter Kloeden
Random attractors and their higher-order regularity properties are studied for stochastic reaction–diffusion equations on time-varying domains. Some new a priori estimates for the difference of solutions near the initial time and the continuous dependence in initial data in H01 are proved. Then attraction of the random attractors in the higher integrability space L2+δ for any δ∈[0,∞) and the regular
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Dynamics of drainage under stochastic rainfall in river networks Stoch. Dyn. (IF 0.742) Pub Date : 2020-03-02 Jorge M Ramirez; Corina Constantinescu
We consider a linearized dynamical system modeling the flow rate of water along the rivers and hillslopes of an arbitrary watershed. The system is perturbed by a random rainfall in the form of a compound Poisson process. The model describes the evolution, at daily time scales, of an interconnected network of linear reservoirs and takes into account the differences in flow celerity between hillslopes
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