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The most likely transition path for a class of distribution-dependent stochastic systems Stoch. Dyn. (IF 1.1) Pub Date : 2023-11-24 Wei Wei, Jianyu Hu
Distribution-dependent stochastic dynamical systems arise widely in engineering and science. We consider a class of such systems which model the limit behaviors of interacting particles moving in a vector field with random fluctuations. We aim to examine the most likely transition path between equilibrium stable states of the vector field. In the small noise regime, the action functional does not involve
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Dynamics of a stochastic phytoplankton–zooplankton system with defensive and offensive effects Stoch. Dyn. (IF 1.1) Pub Date : 2023-11-23 Yi Wang, Qing Guo, Min Zhao, Chuanjun Dai, He Liu
In this paper, we propose a stochastic phytoplankton–zooplankton system considering phytoplankton defensive and zooplankton offensive effects. The aim of this paper is to study the effects of environmental fluctuations on plankton population dynamics. We prove the existence, uniqueness and stochastically ultimately boundedness of global positive solutions, and the extinction and persistence in the
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Identifying stochastic governing equations from data of the most probable transition trajectories Stoch. Dyn. (IF 1.1) Pub Date : 2023-11-21 Jian Ren, Xiaoli Chen
Extracting the governing stochastic differential equation model from elusive data is crucial to understand and forecast dynamics for various systems. We devise a method to extract the drift term and estimate the diffusion coefficient of a governing stochastic dynamical system, from its time-series data for the most probable transition trajectory. By the Onsager–Machlup theory, the most probable transition
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Stochastic dynamics and data science Stoch. Dyn. (IF 1.1) Pub Date : 2023-11-18 Ting Gao, Jinqiao Duan
Recent advances in data science are opening up new research fields and broadening the range of applications of stochastic dynamical systems. Considering the complexities in real-world systems (e.g., noisy data sets and high dimensionality) and challenges in mathematical foundation of machine learning, this review presents two perspectives in the interaction between stochastic dynamical systems and
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Data-driven method to extract mean exit time and escape probability for dynamical systems driven by Lévy noises Stoch. Dyn. (IF 1.1) Pub Date : 2023-11-18 Linghongzhi Lu, Yang Li, Xianbin Liu
Complex dynamical systems have been investigated through many data-driven methods with easily accessible and massive data from observations, experiments or simulations in recent decades. However, few works dealt with the stochastical non-Gaussian perturbation case. In this paper, for a class of systems perturbed by non-Gaussian α-stable Lévy noises, we devise a data-driven approach to extract the mean
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Approximations of Lévy processes by integrated fast oscillating Ornstein–Uhlenbeck processes Stoch. Dyn. (IF 1.1) Pub Date : 2023-11-08 Lingyu Feng, Ting Gao, Ting Li, Zhongjie Lin, Xianming Liu
In this paper, we study a smooth approximation of an arbitrary càdlàg Lévy process. Such approximation processes are known as integrated fast oscillating Ornstein–Uhlenbeck (OU) processes. We know that approximating processes are continuous, while the limit of processes may be discontinuous, so convergence in uniform topology or Skorokhod J1-topology will not hold in general. Therefore, we establish
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On the coercivity condition in the learning of interacting particle systems Stoch. Dyn. (IF 1.1) Pub Date : 2023-11-07 Zhongyang Li, Fei Lu
In the inference for systems of interacting particles or agents, a coercivity condition ensures the identifiability of the interaction kernels, providing the foundation of learning. We prove the coercivity condition for stochastic systems with an arbitrary number of particles and a class of kernels such that the system of relative positions is ergodic. When the system of relative positions is stationary
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On the limit distribution for stochastic differential equations driven by cylindrical non-symmetric α-stable Lévy processes Stoch. Dyn. (IF 1.1) Pub Date : 2023-11-07 Ting Li, Hongbo Fu, Xianming Liu
This paper deals with the limit distribution for a stochastic differential equation driven by a non-symmetric cylindrical α-stable process. Under suitable conditions, it is proved that the solution of this equation converges weakly to that of a stochastic differential equation driven by a Brownian motion in the Skorohod space as α→2. Also, the rate of weak convergence, which depends on 2−α, for the
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An optimal estimate for linear reaction subdiffusion equations with Neumann boundary conditions Stoch. Dyn. (IF 1.1) Pub Date : 2023-11-03 Xiujun Cheng, Wenzhuo Xiong, Huiru Wang
In this paper, we apply classical non-uniform L1 formula and the compact difference scheme for solving linear fractional systems with Neumann boundary conditions. A novelty and simple demonstration strategy is presented on the convergence analysis in the discrete maximum norm. Moreover, based on the special properties of the resulting coefficient matrix, diagonalization technique and discrete cosine
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Functional equations for the stochastic exponential Stoch. Dyn. (IF 1.1) Pub Date : 2023-08-17 Besik Chikvinidze, Michael Mania, Revaz Tevzadze
In this paper, we consider two versions of functional equations for the stochastic exponential. One equation for a function of a semimartingale and its square characteristic and the second for non-anticipative functionals. A martingale characterization of the general solutions of these equations is given.
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The asymptotic behavior of solutions for stochastic evolution equations with pantograph delay Stoch. Dyn. (IF 1.1) Pub Date : 2023-08-17 Yarong Liu, Yejuan Wang, Tomas Caraballo
The polynomial stability problem of stochastic delay differential equations has been studied in recent years. In contrast, there are relatively few works on stochastic partial differential equations with pantograph delay. The present paper is devoted to investigating large-time asymptotic properties of solutions for stochastic pantograph delay evolution equations with nonlinear multiplicative noise
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Stochastic Newton equations in the strong potential limit for the multi-dimensional case Stoch. Dyn. (IF 1.1) Pub Date : 2023-08-17 Song Liang
We consider a type of stochastic Newton equations in multi-dimension, with single-well potential functions, and study the limiting behaviors of their solution processes when the coefficients of the potentials diverge to infinity. The explicit formulations of the limiting processes are also given, by introducing several new stochastic processes. Especially, different from the one-dimensional case, the
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Uniqueness and statistical properties of the Gibbs state on general one-dimensional lattice systems with Markovian structure Stoch. Dyn. (IF 1.1) Pub Date : 2023-07-14 Victor Vargas
Let M be a compact metric space and X=Mℕ, we consider a set of admissible sequences XA,I⊂X determined by a continuous admissibility function A:M×M→ℝ and a compact set I⊂ℝ. Given a Lipschitz continuous potential φ:XA,I→ℝ, we prove uniqueness of the Gibbs state μφ and we show that it is a Gibbs–Bowen measure and satisfies a central limit theorem.
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Global well-posedness for the nonlinear generalized parabolic Anderson model equation Stoch. Dyn. (IF 1.1) Pub Date : 2023-07-17 Qi Zhang
We study the global existence of the singular nonlinear parabolic Anderson model equation on 2-dimensional tours 𝕋2. The method is based on paracontrolled distribution and renormalization. After splitting the original nonlinear parabolic Anderson model equation into two simple equations, we prove the global well-posedness by some a priori estimates and smooth approximations. Furthermore, we prove
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Remotely almost periodicity for SDEs under the framework of evolution system Stoch. Dyn. (IF 1.1) Pub Date : 2023-07-13 Ye-Jun Chen, Hui-Sheng Ding
In this paper, we introduce the concepts of 𝜃-remotely almost periodic processes and remotely almost periodicity in distribution. Under the framework of evolution system, we establish 𝜃-remotely almost periodicity and remotely almost periodicity in distribution for solutions to stochastic differential equations (SDEs) dX(t)=A(t)X(t)dt+F(t,X(t))dt+G(t,X(t))dW(t),t∈ℝ in infinite dimensions. Our main
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Theoretical analysis and numerical approximation for the stochastic thermal quasi-geostrophic model Stoch. Dyn. (IF 1.1) Pub Date : 2023-07-05 Dan Crisan, Darryl D. Holm, Oana Lang, Prince Romeo Mensah, Wei Pan
This paper investigates the mathematical properties of a stochastic version of the balanced 2D thermal quasigeostrophic (TQG) model of potential vorticity dynamics. This stochastic TQG model is intended as a basis for parametrization of the dynamical creation of unresolved degrees of freedom in computational simulations of upper ocean dynamics when horizontal buoyancy gradients and bathymetry affect
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Public private partnerships contract under moral hazard and ambiguous information Stoch. Dyn. (IF 1.1) Pub Date : 2023-06-29 El Mountasar Billah Bouhadjar, Mohamed Mnif
This paper studies optimal Public Private Partnerships contract between a public entity and a consortium, with the possibility for the public to stop the contract. The public (“she”) pays a continuous rent to the consortium (“he”), while the latter gives a response characterized by his effort. Usually, the public cannot observe the effort done by the consortium, in addition, the law of the Agent’s
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Infinite horizon multi-dimensional BSDE with oblique reflection and switching problem Stoch. Dyn. (IF 1.1) Pub Date : 2023-06-29 Brahim El Asri, Nacer Ourkiya
This paper studies a system of multi-dimensional reflected backward stochastic differential equations (RBSDEs) with oblique reflections in infinite horizon associated to switching problems. The existence and uniqueness of the adapted solution is obtained by using a method based on a combination of penalization, verification and contraction property.
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Invariant measure for 2D stochastic Cahn–Hilliard–Navier–Stokes equations Stoch. Dyn. (IF 1.1) Pub Date : 2023-06-20 Zhaoyang Qiu, Huaqiao Wang, Daiwen Huang
In this paper, we investigate the stochastic Cahn–Hilliard–Navier–Stokes equations in two-dimensional spaces. Applying the Maslowski–Seidler method, we establish the existence of invariant measure in state space Lx2×H1 with the weak topology. We also prove the existence of global pathwise solutions using the stochastic compactness argument.
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Singular limits for stochastic equations Stoch. Dyn. (IF 1.1) Pub Date : 2023-06-21 Dirk Blömker, Jonas M. Tölle
We study singular limits of stochastic evolution equations in the interplay of disappearing strength of the noise and insufficient regularity, where the equation in the limit with noise would not be defined due to lack of regularity. We recover previously known results on vanishing small noise with increasing roughness, but our main focus is to study for fixed noise the singular limit where the leading
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Uniformity of singular value exponents for typical cocycles Stoch. Dyn. (IF 1.1) Pub Date : 2023-06-21 Yexing Chen, Yongluo Cao, Rui Zou
Let 𝒜 be a GLd(ℝ)-valued cocycle over a subshift of finite type. Under a certain twisting assumption, we prove that 𝒜 has a uniform Lyapunov exponent if and only if the largest Lyapunov exponent of 𝒜 at all periodic points equals. Under the typicality assumption, we give two checkable criteria for deciding whether 𝒜 has uniform singular value exponents.
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Climate change for global warming 1.5∘C under the influence of multiplicative Gaussian noise Stoch. Dyn. (IF 1.1) Pub Date : 2023-06-16 Xingyuan Bu
We propose a stochastic energy balance differential equation with multiplicative Gaussian noise, which better captures the influence of the atmosphere as external noise on climate change. Meanwhile, we apply the Milstein method with stronger convergence to approximate the stochastic climate change trajectory. Further, the numerical approach can efficiently calculate two exit concepts: the mean first
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Stochastic stability for partially hyperbolic diffeomorphisms with mostly expanding and mostly contracting centers Stoch. Dyn. (IF 1.1) Pub Date : 2023-06-16 Zeya Mi
We prove the stochastic stability of an open class of diffeomorphisms, each of which admits a partially hyperbolic splitting TM=Eu⊕Ecu⊕Ecs such that any Gibbs u-state admits only positive (respectively, negative) Lyapunov exponents along Ecu (respectively, Ecs).
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Periodic measures for a class of SPDEs with regime-switching Stoch. Dyn. (IF 1.1) Pub Date : 2023-06-16 Chun Ho Lau, Wei Sun
We use the variational approach to investigate periodic measures for a class of stochastic partial differential equations (SPDEs) with regime-switching. The hybrid system is driven by degenerate Lévy noise. We use the Lyapunov function method to study the existence of periodic measures and show the uniqueness of periodic measures by establishing the strong Feller property and irreducibility of the
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Stochastic averaging for a completely integrable Hamiltonian system with fractional Brownian motion Stoch. Dyn. (IF 1.1) Pub Date : 2023-05-13 Ruifang Wang, Yong Xu, Bin Pei
This paper proposes an effective approximation result for the behavior of a small transversal perturbation to a completely integrable stochastic Hamiltonian system on a symplectic manifold. We derive an averaged stochastic differential equations (SDEs) in the action space for the action component of the perturbed system, where the averaged drift coefficient is characterized by the averages of that
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Well-posedness of a system of SDEs driven by jump random measures Stoch. Dyn. (IF 1.1) Pub Date : 2023-05-13 Ying Jiao, Nikolaos Kolliopoulos
We establish well-posedness for a class of systems of SDEs with non-Lipschitz coefficients in the diffusion and jump terms and with two sources of interdependence: a monotone function of all the components in the drift of each SDE and the correlation between the driving Brownian motions and jump random measures. Pathwise uniqueness is derived by employing some standard techniques. Then, we use a comparison
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Deviation and concentration inequalities for dynamical systems with subexponential decay of correlations Stoch. Dyn. (IF 1.1) Pub Date : 2023-04-26 Christophe Cuny, Jérôme Dedecker, Florence Merlevède
We obtain large and moderate deviation estimates, as well as concentration inequalities, for a class of nonuniformly expanding maps with stretched exponential decay of correlations. In the large deviation regime, we also exhibit examples showing that the obtained upper bounds are essentially optimal.
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Density of nonzero exponent of contraction for pinching cocycles in Hom(S1) Stoch. Dyn. (IF 1.1) Pub Date : 2023-04-21 Catalina Freijo, Karina Marin
We consider pinching cocycles taking values in the space of homeomorphisms of the circle over an hyperbolic base. Using the invariance principle of Malicet, we prove that the cocycles having nonzero exponents of contraction are dense. In this paper, we generalize some common notions an results known of linear cocycles and cocycles of diffeomorphisms, to the nonlinear non-differentiable case.
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Kolmogorov bounds in the CLT of the LSE for Gaussian Ornstein Uhlenbeck processes Stoch. Dyn. (IF 1.1) Pub Date : 2023-04-11 Maoudo Faramba Balde, Rachid Belfadli, Khalifa Es-Sebaiy
In this paper, we consider the Ornstein–Uhlenbeck (OU) process defined as solution to the equation dXt=−𝜃Xtdt+dGt, X0=0, where {Gt,t≥0} is a Gaussian process with stationary increments, whereas 𝜃>0 is unknown parameter to be estimated. We provide an upper bound in Kolmogorov distance for normal approximation of the least squares estimator 𝜃̃T of the drift parameter 𝜃 on the basis of the continuous
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The two-barrier escape problem for compound renewal processes with two-sided jumps Stoch. Dyn. (IF 1.1) Pub Date : 2023-03-21 Javier Villarroel, Juan A. Vega
We consider the problem of determining two-sided exit probabilities for a compound renewal process with drift and two-sided jumps. In certain cases the problem can be reduced to determining the distribution of a random sum of i.i.d. random variables. In a general situation this problem is reduced to solving a certain integral equation. We obtain explicit expressions for the escape probability for several
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Ergodicity of exclusion semigroups constructed from quantum Bernoulli noises Stoch. Dyn. (IF 1.1) Pub Date : 2023-03-13 Jinshu Chen, Shexiang Hai
Quantum Bernoulli noises (QBN) are the family of annihilation and creation operators acting on Bernoulli functionals, which satisfy the canonical anti-commutation relation (CAR) in equal time. This paper aimed to discuss the classical reduction and ergodicity of quantum exclusion semigroups constructed by QBN. We first study the classical reduction of the quantum semigroups to an Abelian algebra of
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Asymptotic behavior of maximum likelihood estimators for Ornstein–Uhlenbeck process with large linear drift Stoch. Dyn. (IF 1.1) Pub Date : 2023-03-13 Xuekang Zhang
In this paper, we study the asymptotic behavior of maximum likelihood estimators for Ornstein–Uhlenbeck process with large linear drift dXt=−1𝜀(𝜃Xt−𝜀12ν)dt+dBt, 0≤t≤T, where 𝜃,ν∈ℝ, and {Bt}t≥0 is a given standard Brownian motion. The law of iterated logarithm, consistency and asymptotic distributions of the estimators are discussed based on the continuous observation {Xt}t∈[0,T] as 𝜀→0.
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A Monte Carlo algorithm for multiple stochastic integrals of stable processes Stoch. Dyn. (IF 1.1) Pub Date : 2023-02-10 Anirban Das, Manfred Denker, Anna Levina, Lucia Tabacu
In this paper, we provide a Monte Carlo method to calculate multiple stochastic integrals which is based on a.s. distributional convergence.
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Nonexistence of observable chaos and its robustness in strongly monotone dynamical systems Stoch. Dyn. (IF 1.1) Pub Date : 2023-02-10 Yi Wang, Jinxiang Yao
For strongly monotone dynamical systems on a Banach space, we show that the largest Lyapunov exponent λmax>0 holds on a shy set in the measure-theoretic sense. This exhibits that strongly monotone dynamical systems admit no observable chaos, the notion of which was formulated by L.S. Young. We further show that such phenomenon of no observable chaos is robust under the C1-perturbation of the systems
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Physical measures of asymptotically autonomous dynamical systems Stoch. Dyn. (IF 1.1) Pub Date : 2023-02-10 Julian Newman, Peter Ashwin
Although chaotic attractors for autonomous dynamical systems show sensitive dependence on initial conditions, they also typically support a physical or natural measure that characterizes the statistical behavior of almost all initial conditions near the attractor with respect to a background measure such as Lebesgue. In this paper, we identify conditions under which a nonautonomous system that limits
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Unstable manifolds for rough evolution equations Stoch. Dyn. (IF 1.1) Pub Date : 2023-02-03 Hongyan Ma, Hongjun Gao
In this paper, we consider a class of rough nonlinear evolution equations driven by infinite-dimensional γ-Hölder rough paths with γ ∈ (1/3,1/2]. First, we give a proper integral with respect to infinite-dimensional γ-Hölder rough paths by using rough paths theory. Second, we obtain the global in time solution and random dynamical system of rough evolution equation. Finally, we derive the existence
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LaSalle-type stationary oscillation principle for stochastic affine periodic systems Stoch. Dyn. (IF 1.1) Pub Date : 2023-02-03 Xiaomeng Jiang, Yong Li, Xue Yang
In this paper, we establish a LaSalle-type stationary oscillation principle to obtain the existence and stability of affine periodic solutions in distribution for stochastic differential equations. As applications, we show the existence and asymptotic stability of stochastic affine periodic solutions in distribution via Lyapunov’s method.
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Entropy estimates for uniform attractors of 2D Navier–Stokes equations with weakly normal measures Stoch. Dyn. (IF 1.1) Pub Date : 2023-02-03 Yangmin Xiong, Xiaoya Song, Chunyou Sun
This paper aims at the long-time behavior of non-autonomous 2D Navier–Stokes equations with a class of external forces which are H-valued measures in time. We first establish the well-posedness of solutions as well as the existence of a strong uniform attractor, and then pay the main attention on the estimation of 𝜀-entropy for such uniform attractor in the standard energy phase space.
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Mean asymptotic behavior for stochastic Kuramoto–Sivashinshy equation in Bochner spaces Stoch. Dyn. (IF 1.1) Pub Date : 2023-02-03 Shuyuan Fan, Xiaopeng Chen
This paper is concerned with the mean asymptotic behavior of the Kuramoto–Sivashinshy equation with stochastic perturbation. We define the mean random dynamical systems for the stochastic Kuramoto–Sivashinshy equation in Bochner spaces. Then we obtain the so-called weak pullback mean random attractor for the stochastic Kuramoto–Sivashinshy equation with odd initial conditions.
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Small perturbations may change the sign of Lyapunov exponents for linear SDEs Stoch. Dyn. (IF 1.1) Pub Date : 2023-02-03 Xianjin Cheng, Zhenxin Liu, Lixin Zhang 3 , *
In this paper, we study the existence of n-dimensional linear stochastic differential equations (SDEs) such that the sign of Lyapunov exponents is changed under an exponentially decaying perturbation. First, we show that the equation with all positive Lyapunov exponents will have n−1 linearly independent solutions with negative Lyapunov exponents under the perturbation. Meanwhile, we prove that the
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Average preserving variation processes in view of optimization Stoch. Dyn. (IF 1.1) Pub Date : 2023-02-03 Rémi Lassalle
In this paper, we investigate specific least action principles for laws of stochastic processes within a framework which stands on filtrations preserving variations. The associated Euler–Lagrange conditions, which we obtain, exhibit a deterministic process in the dynamics aside the canonical martingale term. In particular, taking specific action functionals, extremal processes with respect to those
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Weak mean random attractors for nonautonomous stochastic parabolic equation with variable exponents Stoch. Dyn. (IF 1.1) Pub Date : 2023-02-03 Jiangwei Zhang, Zhiming Liu, Jianhua Huang
In this paper, we consider the asymptotic behavior of solutions for nonautonomous stochastic parabolic equation with nonstandard growth condition driven by nonlinear multiplicative noise for the first time. First, by making use of variational method, we prove the existence and uniqueness of solutions, and then the mean random dynamical systems generated by stochastic parabolic equations with variable
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The β-Delaunay tessellation IV: Mixing properties and central limit theorems Stoch. Dyn. (IF 1.1) Pub Date : 2023-02-03 Anna Gusakova, Zakhar Kabluchko, Christoph Thäle
Various mixing properties of β-, β′- and Gaussian-Delaunay tessellations in ℝd−1 are studied. It is shown that these tessellation models are absolutely regular, or β-mixing. In the β- and the Gaussian case exponential bounds for the absolute regularity coefficients are found. In the β′-case these coefficients show a polynomial decay only. In the background are new and strong concentration bounds on
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Analysis of a microfluidic chemostat model with random dilution ratios Stoch. Dyn. (IF 1.1) Pub Date : 2023-01-25 Jifa Jiang, Xiang Lv
In this paper, we first construct a microfluidic chemostat model for the growth of biofilms and planktonic populations with random dilution ratios and then investigate its dynamical behavior. Using the theory of monotone dynamical systems and the Multiplicative Ergodic Theorem, we show the existence of random attractors and stationary measures, and present Lyapunov exponents for the linearized cocycle
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An approximate approach to fuzzy stochastic differential equations under sub-fractional Brownian motion Stoch. Dyn. (IF 1.1) Pub Date : 2023-01-14 Hossein Jafari, Hamed Farahani
In this paper, we introduce fuzzy stochastic differential equations (FSDEs) driven by sub-fractional Brownian motion (SFBM) which are applied to describe phenomena subjected to randomness and fuzziness simultaneously. The SFBM is an extension of the Brownian motion that retains many properties of fractional Brownian motion (FBM), but not the stationary increments. This property makes SFBM a possible
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First passage time and mean exit time for switching Brownian motion Stoch. Dyn. (IF 1.1) Pub Date : 2023-01-12 Jinying Tong, Ruifang Wu, Qianqian Zhang, Zhenzhong Zhang, Enwen Zhu
In this paper, we consider some properties of switching Brownian motion. Combining the analytic method and probabilistic method, some explicit expressions of density functions, the mean exit time and Laplace transform of exit time are given. This paper reveals how drift coefficients impact the first passage probabilities, scale functions and the mean exit time for switching Brownian motion.
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Convergence of nonlinear filtering for multiscale systems with correlated Lévy noises Stoch. Dyn. (IF 1.1) Pub Date : 2023-01-11 Huijie Qiao
The work concerns nonlinear filtering problems of multiscale systems with Lévy noises in two cases-correlated noises and correlated sensor noises. First of all, we prove that the slow part of the origin system converges to the average system in the uniform mean square sense. Then based on the convergence result, in two cases of correlated Lévy noises and correlated Gaussian noises, we prove that the
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A two-dimensional stochastic fractional non-local diffusion lattice model with delays Stoch. Dyn. (IF 1.1) Pub Date : 2023-01-09 Yejuan Wang, Yu Wang, Xiaoying Han, Peter E. Kloeden
The well-posedness, regularity and general stability of solutions to a two-dimensional stochastic non-local delay diffusion lattice system with a time Caputo fractional operator of order α𝜀(1/2,1) are investigated in Lp spaces for p≥2. First, the global existence and uniqueness of solutions are established by using a temporally weighted norm, the Burkholder–Davis–Gundy inequality and the Banach fixed
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Exponential ergodicity for a stochastic two-layer quasi-geostrophic model Stoch. Dyn. (IF 1.1) Pub Date : 2022-12-30 Giulia Carigi, Jochen Bröcker, Tobias Kuna
Ergodic properties of a stochastic medium complexity model for atmosphere and ocean dynamics are analyzed. More specifically, a two-layer quasi-geostrophic model for geophysical flows is studied, with the upper layer being perturbed by additive noise. This model is popular in the geosciences, for instance to study the effects of a stochastic wind forcing on the ocean. A rigorous mathematical analysis
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Forward–backward stochastic differential equations with delay generators Stoch. Dyn. (IF 1.1) Pub Date : 2022-12-30 Auguste Aman, Harouna Coulibaly, Jasmina Đorđević
In this paper, we prove a result of existence and uniqueness of solutions to coupled forward–backward stochastic differential equations with delayed generators under a Lipschitz condition.
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On the rate of convergence of weighted oscillating ergodic averages Stoch. Dyn. (IF 1.1) Pub Date : 2022-12-30 Ahmad Darwiche, Dominique Schneider
Let (X,𝒜,μ) be a probability space, let T be a contraction on Lp(μ) and let f in Lp(μ), (p>1). In this paper, we provide suitable conditions over sequences (wk), (uk) and (Ak) in such a way that the limit of the weighted ergodic average is limN→∞1AN∑k=0N−1wkTuk(f)=0μ-a.e. We also give applications which concretely prove the effectiveness of the obtained theorems. More precisely, we construct sequences
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The probability of events for stochastic parabolic equations Stoch. Dyn. (IF 1.1) Pub Date : 2022-12-21 Guangying Lv, Jinlong Wei
In this short paper, we focus on the blowup phenomenon of stochastic parabolic equations. We first discuss the probability of the event that the solutions keep positive. Then, the blowup phenomenon in the whole space is considered. The probability of the event that the solutions blow up in finite time is given. Lastly, we obtain the probability of the event that blowup time of stochastic parabolic
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Rate of homogenization for fully-coupled McKean–Vlasov SDEs Stoch. Dyn. (IF 1.1) Pub Date : 2022-12-21 Zachary William Bezemek, Konstantinos Spiliopoulos
In this paper, we consider a fully-coupled slow–fast system of McKean–Vlasov stochastic differential equations with full dependence on the slow and fast component and on the law of the slow component and derive convergence rates to its homogenized limit. We do not make periodicity assumptions, but we impose conditions on the fast motion to guarantee ergodicity. In the course of the proof we obtain
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Stochastic rotating waves Stoch. Dyn. (IF 1.1) Pub Date : 2022-12-19 Christian Kuehn, James MacLaurin, Giulio Zucal
Stochastic dynamics has emerged as one of the key themes ranging from models in applications to theoretical foundations in mathematics. One class of stochastic dynamics problems that has recently received considerable attention are traveling wave patterns occurring in stochastic partial differential equations (SPDEs). Here, one is interested in how deterministic traveling waves behave under stochastic
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Approximation for a generalized Langevin equation with high oscillation in time and space Stoch. Dyn. (IF 1.1) Pub Date : 2022-12-13 Dong Su, Wei Wang
This paper derives an approximation for a generalized Langevin equation driven by a force with random oscillation in time and periodic oscillation in space. By a diffusion approximation and the weak convergence of periodic oscillation function, the solution of the generalized Langevin equation is shown to converge in distribution to the solution of a stochastic partial differential equations (SPDEs)
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Bohl–Perron theorem for random dynamical systems Stoch. Dyn. (IF 1.1) Pub Date : 2022-12-13 Nguyen Huu Du, Tran Manh Cuong, Ta Thi Trang
In this paper, we consider the Bohl–Perron Theorem for linear random dynamical systems. We prove that the tempered exponential stability of a linear co-cycle is equivalent to the boundedness of solutions for inherit difference equation. Paper also proves a similar concept for co-cycle admitting a tempered exponential dichotomy.
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Dynamics of a multi-species lottery competition model in stochastic environments Stoch. Dyn. (IF 1.1) Pub Date : 2022-12-06 Jiaqi Cheng, Xiaoying Han, Ming Liao
An N-dimensional lottery model for competition among N≥2 ecological species in stochastic environments is studied under the i.i.d. assumption. First, a system of nonlinear stochastic differential equations (SDEs) is developed as the diffusion approximation for the discrete lottery model. Then the existence and uniqueness of positive and bounded global solutions, as well as long-term dynamics for the
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Asymptotic pressure on some self-similar trees Stoch. Dyn. (IF 1.1) Pub Date : 2022-12-06 Karl Petersen, Ibrahim Salama
The vertices of the Cayley graph of a finitely generated semigroup form a set of sites which can be labeled by elements of a finite alphabet in a manner governed by a nonnegative real interaction matrix, respecting nearest neighbor adjacency restrictions. To the set of these configurations one can associate a pressure, which is defined as the limit, when it exists, of averages of the logarithm of the
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Some perpetual integral functionals of the three-dimensional Bessel process Stoch. Dyn. (IF 1.1) Pub Date : 2022-11-29 Yukihiro Tsuzuki
We compute the Laplace transforms of some integral functionals of the three-dimensional Bessel process in terms of modified Bessel functions, Gauss’ hypergeometric functions, and confluent hypergeometric functions. Some new results are obtained, and several established results, such as Dufresne’s perpetuity and a particular case of its translated version, are recovered. In particular, we derive the
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Arcsine and Darling–Kac laws for piecewise linear random interval maps Stoch. Dyn. (IF 1.1) Pub Date : 2022-11-19 Genji Hata, Kouji Yano
We give examples of piecewise linear random interval maps satisfying arcsine and Darling–Kac laws, which are analogous to Thaler’s arcsine and Aaronson’s Darling–Kac laws for the Boole transformation. They are constructed by random switch of two piecewise linear maps with attracting or repelling fixed points, which behave as if they were indifferent fixed points of a deterministic map.