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Lower and upper bounds for the explosion times of a system of semilinear SPDEs Stochastics (IF 0.9) Pub Date : 2024-03-12 S. Sankar, Manil T. Mohan, S. Karthikeyan
In this paper, we obtain lower and upper bounds for the blow-up times for a system of semilinear stochastic partial differential equations. Under suitable assumptions, lower and upper bounds of the...
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Asymptotics for ruin probabilities of a dependent delayed-claim risk model with general investment returns and diffusion Stochastics (IF 0.9) Pub Date : 2024-03-12 Ruonan Yang, Jiangyan Peng, Lei Zou
In this paper, we study a delayed-claim insurance risk model perturbed by diffusion with general investment returns, in which each main claim may induce a delayed claim. Assume that the main claim ...
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Risk-sensitive discounted Markov decision processes with unbounded reward functions and Borel spaces Stochastics (IF 0.9) Pub Date : 2024-03-12 Xin Guo
This paper attempts to study the risk-sensitive discounted discrete-time Markov decision processes in Borel spaces, in which the reward functions are allowed to be unbounded from above and from bel...
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Asymptotics for ruin probabilities in a bidimensional discrete-time risk model with dependent and consistently varying tailed net losses Stochastics (IF 0.9) Pub Date : 2024-03-12 Hongxia Wang, Qi Su, Yang Yang
Consider an insurer who operates two lines of businesses and hence receives two types of insurance net losses. In the bidimensional discrete-time risk model with a constant interest rate, the net l...
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First-exit-time problems for two-dimensional Wiener and Ornstein–Uhlenbeck processes through time-varying ellipses Stochastics (IF 0.9) Pub Date : 2024-03-12 Antonio Di Crescenzo, Virginia Giorno, Amelia G. Nobile, Serena Spina
We study the first-exit-time problem for the two-dimensional Wiener and Ornstein–Uhlenbeck processes through time-varying ellipses which run according to specific rules depending on the processes. ...
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Asymptotic properties for the parameter estimation in stochastic (functional) differential equations with Hölder drift Stochastics (IF 0.9) Pub Date : 2024-03-12 Yanyan Hu, Fubao Xi, Min Zhu
In this paper, by taking Zvonkin's transformation, we investigate parameter estimation for a class of multidimensional stochastic differential equations with small perturbation parameters in diffus...
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Limit theorems for a class of processes generalizing the U-empirical process Stochastics (IF 0.9) Pub Date : 2024-03-12 Salim Bouzebda, Inass Soukarieh
In this paper, we develop theory and tools for studying U-processes, a natural higher-order generalization of the empirical processes. We introduce a class of random discrete U-measures that genera...
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Stochastic near-optimal controls for treatment and vaccination in a COVID-19 model with transmission incorporating Lévy jumps Stochastics (IF 0.9) Pub Date : 2024-03-12 Driss Bouggar, Mohamed El Fatini, Bouchra Nasri, Roger Petersson, Idriss Sekkak
The COVID-19 pandemic has triggered a groundbreaking reliance on mathematical modelling as an important tool for studying and managing the spread of the virus since its emergence. Public health pre...
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Optimal exercise of American options under time-dependent Ornstein–Uhlenbeck processes Stochastics (IF 0.9) Pub Date : 2024-03-12 Abel Azze, Bernardo D'Auria, Eduardo García-Portugués
We study the barrier that gives the optimal time to exercise an American option written on a time-dependent Ornstein–Uhlenbeck process, a diffusion often adopted by practitioners to model commodity...
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Criteria for what makes a local optional martingale a true martingale Stochastics (IF 0.9) Pub Date : 2024-01-31 Mohamed Abdelghani, Alexander Melnikov
What makes an optional stochastic exponential a true optional martingale in a probability space where the underlying filtration is not right continuous nor complete. In this paper, we are going to ...
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On weighted pseudo almost automorphic mild solutions for some mean field stochastic evolution equations Stochastics (IF 0.9) Pub Date : 2024-01-09 Moustapha Dieye, Amadou Diop, Mamadou Moustapha Mbaye, Mark A. McKibben
When the evolution family is hyperbolic and satisfies the Acquistapace-Terreni conditions, the existence and uniqueness of an almost automorphic mild solution and a weighted pseudo almost automorph...
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Central limit theorem for bifurcating Markov chains: the mother-daughters triangles case Stochastics (IF 0.9) Pub Date : 2024-01-07 S. Valère Bitseki Penda
The main objective of this article is to establish a central limit theorem for additive three-variable functionals of bifurcating Markov chains. We thus extend the central limit theorem under point...
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On the S-asymptotically ω-periodic mild solutions for multi-term time fractional measure integro-differential equations Stochastics (IF 0.9) Pub Date : 2024-01-07 Haide Gou
This paper deals with a class of nonlocal problem for multi-term time-fractional measure integro-differential evolution equations of mixed type in Hilbert spaces. Firstly, we introduce the concept ...
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Low-dimensional Cox-Ingersoll-Ross process Stochastics (IF 0.9) Pub Date : 2024-01-10 Yuliya Mishura, Andrey Pilipenko, Anton Yurchenko-Tytarenko
The present paper investigates Cox-Ingersoll-Ross (CIR) processes of dimension less than 1, with a focus on obtaining an equation of a new type including local times for the square root of the CIR ...
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Complete convergence and complete moment convergence for weighted sums of random variables satisfying generalized Rosenthal type inequalities and an application Stochastics (IF 0.9) Pub Date : 2024-01-01 Xiaoqian Zheng, Chunhua Wang, Xuejun Wang
This article mainly investigates the complete convergence and complete moment convergence for weighted sums of random variables satisfying generalized Rosenthal type inequalities, which improves th...
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The Donsker delta function and local time for McKean–Vlasov processes and applications Stochastics (IF 0.9) Pub Date : 2023-12-06 Nacira Agram, Bernt Øksendal
The purpose of this paper is to establish a stochastic differential equation for the Donsker delta measure of the solution of a McKean–Vlasov (mean-field) stochastic differential equation.If the Do...
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Different topological solution structures in a two-dimensional controlled ruin problem depending on the optimization criterion Stochastics (IF 0.9) Pub Date : 2023-12-05 Peter Grandits, Maike Klein
We consider two insurance companies with wealth processes given by independent Brownian motions with controllable non-negative drift. The drift rates sum up to 1. The companies aim at finding a str...
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Two-sided Poisson control of linear diffusions Stochastics (IF 0.9) Pub Date : 2023-11-27 Harto Saarinen
We study a class of two-sided optimal control problems of general linear diffusions under a so-called Poisson constraint: the controlling is only allowed at the arrival times of an independent Pois...
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Stationary, Markov, stochastic processes with polynomial conditional moments and continuous paths Stochastics (IF 0.9) Pub Date : 2023-11-20 Paweł J. Szabłowski
We are studying stationary random processes with conditional polynomial moments that allow a continuous path modification. Processes with continuous path modification are important because they are...
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A continuous-time N-interaction random graph model Stochastics (IF 0.9) Pub Date : 2023-11-20 Bettina Porvázsnyik
In this paper a continuous-time evolving random graph model is defined and examined. The main units of the model are complete graphs on N vertices, where N≥3 is a fixed integer. At each birth event...
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Monotone iterative technique for evolution equations with delay and nonlocal conditions in ordered Banach space Stochastics (IF 0.9) Pub Date : 2023-11-14 Haide Gou
In this paper, based on monotone iterative method in the presence of the lower and upper solutions, we investigate the existence and uniqueness of the S-asymptotically ω-periodic mild solutions to ...
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Large deviation principles of nonlinear filtering for McKean-Vlasov stochastic differential equations Stochastics (IF 0.9) Pub Date : 2023-11-15 Huijie Qiao, Shengqing Zhu
In this paper, we study large deviation principles of nonlinear filtering for McKean-Vlasov stochastic differential equations. First of all, we establish the large deviation principle for the space...
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Well-posedness for anticipated backward stochastic Schrödinger equations Stochastics (IF 0.9) Pub Date : 2023-11-09 Zhang Chen, Li Yang
In this paper, we consider the well-posedness for the anticipated backward stochastic Schrödinger equation in a bounded domain or the whole space Rd, which is associated to a stochastic control pro...
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Complete f-moment convergence for sums of asymptotically almost negatively associated random variables with statistical applications Stochastics (IF 0.9) Pub Date : 2023-10-04 Houlin Zhou, Chao Lu, Xuejun Wang
In this paper, we mainly study the complete f-moment convergence for sums of asymptotically almost negatively associated (AANA, for short) random variables and provide an application. A general res...
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Infinite horizon impulse control of stochastic functional differential equations driven by Lévy processes Stochastics (IF 0.9) Pub Date : 2023-10-04 M. Perninge
We consider impulse control of stochastic functional differential equations (SFDEs) driven by Lévy processes under an additional Lp-Lipschitz condition on the coefficients. Our results, which are f...
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A recursive representation for decoupling time-state dependent jumps from jump-diffusion processes Stochastics (IF 0.9) Pub Date : 2023-09-25 Qinjing Qiu, Reiichiro Kawai
We establish a recursive representation that fully decouples jumps from a large class of multivariate inhomogeneous stochastic differential equations with jumps of general time-state dependent unbo...
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Averaging principles for two-time-scale neutral stochastic delay partial differential equations driven by fractional Brownian motions Stochastics (IF 0.9) Pub Date : 2023-09-16 Bin Pei, Yong Xu, Min Han
We prove the validity of averaging principles for two-time-scale neutral stochastic delay partial differential equations (NSDPDEs) driven by fractional Brownian motions (fBms) under two-time-scale formulation. Firstly, in the sense of mean-square convergence, we obtain not only the averaging principles for NSDPDEs involving two-time-scale Markov switching with a single weakly recurrent class but also
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Malliavin derivative of Teugels martingales and mean-field type stochastic maximum principle Stochastics (IF 0.9) Pub Date : 2023-09-11 Gaofeng Zong
We study the mean-field type stochastic control problem where the dynamics is governed by a general Lévy process with moments of all orders. For this, we introduce the power jump processes and the related Teugels martingales and give the Malliavin derivative with respect to Teugels martingales. We derive necessary and sufficient conditions for optimality of our control problem in the form of a mean-field
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Asymptotics and criticality for a space-dependent branching process Stochastics (IF 0.9) Pub Date : 2023-09-13 Ilie Grigorescu, Min Kang
We investigate a non-conservative semigroup (St)t≥0(St)t≥0 determined by a branching process tracing the evolution of particles moving in a domain in RdRd . When a particle is killed at the boundary, a new generation of particles with mean number K¯ is born at a random point in the domain. Between branching, the particles are driven by a diffusion process with Dirichlet boundary conditions. According
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Solving stochastic equations with unbounded nonlinear perturbations Stochastics (IF 0.9) Pub Date : 2023-09-13 Mohamed Fkirine, Said Hadd
This paper is interested in semilinear stochastic equations having unbounded nonlinear perturbations in the deterministic part and/or in the random part. Moreover, the linear part of these equations is governed by a not necessarily analytic semigroup. The main difficulty with these equations is how to define the concept of mild solutions due to the chosen type of unbounded perturbations. To overcome
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The asymptotic equipartition property for a special Markov random field Stochastics (IF 0.9) Pub Date : 2023-09-11 Zhiyan Shi, Xiaoyu Zhu
The asymptotic equipartition property (AEP) plays an important role in establishing lossless source coding theorems and asymptotic coding theorems through the concepts of typical sets and typical sequences in information theory. In this paper, we study the generalized asymptotic equipartition property in the form of moving average for N bifurcating Markov chains indexed by an N-branch Cayley tree,
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Collective epidemics with asymptomatics and functional infection rates Stochastics (IF 0.9) Pub Date : 2023-09-07 Claude Lefèvre, Matthieu Simon
ABSTRACT This paper discusses a generalized SIR epidemic model that incorporates infectives with or without symptoms, allows arbitrary distributions for infectious periods and assumes infection rates depending on the current size of susceptibles. Our interest lies in the joint distribution of the state of the population and the severity of the disease at the end of infection. The approach is based
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Hitting times for sticky skew CIR process Stochastics (IF 0.9) Pub Date : 2023-09-07 Haoyan Zhang, Yingxu Tian
In this paper, we consider an extended skew CIR processes with sticky points, which is referred to as the sticky skew CIR process. We first calculate the infinitesimal generator and its domain. To explore its trajectory properties, we compute the Laplace transforms and the expectations of first hitting times over a constant boundary. The solutions of Laplace transforms are expressed in terms of Tricomi
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Convergence of densities of spatial averages of the parabolic Anderson model driven by colored noise Stochastics (IF 0.9) Pub Date : 2023-07-26 Sefika Kuzgun, David Nualart
In this paper, we present a rate of convergence in the uniform norm for the densities of spatial averages of the solution to the d-dimensional parabolic Anderson model driven by a Gaussian multiplicative noise, which is white in time and has a spatial covariance given by the Riesz kernel. The proof is based on the combination of Malliavin calculus techniques and the Stein's method for normal approximations
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Asymptotics for sum-ruin probabilities of a bidimensional risk model with heavy-tailed claims and stochastic returns Stochastics (IF 0.9) Pub Date : 2023-07-20 Zhangting Chen, Mingjun Li, Dongya Cheng
This paper considers a bidimensional risk model with geometric Lévy price processes and dependent heavy-tailed claims, where the two claim-number processes generated by the two different lines of business are almost arbitrarily dependent. When the distributions of the claims are subexponential with a positive lower Matuszewska index, an asymptotic formula for the finite-time sum-ruin probability is
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Complete f-moment convergence for weighted sums of asymptotically almost negatively associated random variables and its application in semiparametric regression models Stochastics (IF 0.9) Pub Date : 2023-07-04 Junjun Lang, Jibing Qi, Fei Zhang, Xuejun Wang
In this paper, we investigate the complete f-moment convergence for weighted sums of asymptotically almost negatively associated (AANA, for short) random variables. Our results improve and generali...
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Estimation and asymptotics for vector autoregressive models with unit roots and Markov switching trends Stochastics (IF 0.9) Pub Date : 2023-06-27 Maddalena Cavicchioli
We provide a formal definition of an M-state multivariate Markov switching (MS) trend, describe its asymptotic distribution, and consider vector autoregressive processes with MS trends which cont...
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Causal predictability between stochastic processes and filtrations Stochastics (IF 0.9) Pub Date : 2023-05-29 Ana Merkle
In this paper we further develop a notion of causal predictability defined in [A. Merkle, Predictability and Uniqueness of Weak Solutions of Stochastic Differential Equations, Analele Stiintifice a...
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On the stochastic differentiability of noncausal processes with respect to the process with quadratic variation Stochastics (IF 0.9) Pub Date : 2023-05-26 Kiyoiki Hoshino
Let (Vt)t∈[0,L] be a stochastic process with quadratic variation on a probability space (Ω,F,P) and Q(∋0) a dense subset of [0,L], where [0,L] is regarded as the infinite interval [0,∞) when ...
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Moderate deviations of generalized N-urn Ehrenfest models Stochastics (IF 0.9) Pub Date : 2023-05-23 Lirong Ren, Xiaofeng Xue
This paper is a further investigation of the generalized N-urn Ehrenfest model introduced in Xue [Hydrodynamics of the generalized N-urn Ehrenfest model, Potential Anal. 2022. Online. Available at ...
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On 1-point densities for Arratia flows with drift Stochastics (IF 0.9) Pub Date : 2023-05-12 Andrey A. Dorogovtsev, Mykola B. Vovchanskyi
We show that if drift coefficients of Arratia flows converge in L1(R) or L∞(R) then the 1-point densities associated with these flows converge to the density for the flow with the limit drift. Th...
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Strong solutions for the stochastic Allen-Cahn-Navier-Stokes system Stochastics (IF 0.9) Pub Date : 2023-04-19 Gabriel Deugoué, Aristide Ndongmo Ngana, Theodore Tachim Medjo
We study in this article a stochastic version of a coupled Allen-Cahn-Navier-Stokes model on a bounded domain of Rd,d=2,3Rd,d=2,3 . The model consists of the Navier-Stokes equations for the velocity, coupled with an Allen-Cahn model for the order (phase) parameter. We prove the existence and uniqueness of a local maximal strong solution when the initial data (u0,ϕ0) takes values in H1×H2. Moreover
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Reflecting image-dependent SDEs in Wasserstein space and large deviation principle Stochastics (IF 0.9) Pub Date : 2023-04-13 Xue Yang
In this article, we study a class of reflecting stochastic differential equations whose coefficients depend on image measures of solutions under a given initial measure in Wasserstein space P2. By...
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A large deviation principle for fluids of third grade Stochastics (IF 0.9) Pub Date : 2023-02-09 Adilson Almeida, Fernanda Cipriano
ABSTRACT This article establishes a large deviation principle for a non-Newtonian fluid of differential type, filling a two-dimensional non-axisymmetric bounded domain with slip boundary conditions. More precisely, we show that the solutions of small stochastic white noise perturbations of the third grade fluid equations converges to the deterministic solution, as the intensity of the noise goes to
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Scaling limits of bisexual Galton–Watson processes Stochastics (IF 0.9) Pub Date : 2023-02-06 Vincent Bansaye, Maria-Emilia Caballero, Sylvie Méléard, Jaime San Martín
Bisexual Galton–Watson processes are discrete Markov chains where reproduction events are due to mating of males and females. Owing to this interaction, the standard branching property of Galton–Watson processes is lost. We prove tightness for conveniently rescaled bisexual Galton–Watson processes, based on recent techniques developed in [V. Bansaye, M.E. Caballero, and S. Méléard, Scaling limits of
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Large time behaviour of semilinear stochastic partial differential equations perturbed by a mixture of Brownian and fractional Brownian motions Stochastics (IF 0.9) Pub Date : 2023-01-23 Marco Dozzi, Ekaterina T. Kolkovska, José A. López-Mimbela, Rim Touibi
We study the trajectorywise blowup behaviour of a semilinear partial differential equation that is driven by a mixture of multiplicative Brownian and fractional Brownian motion, modelling different types of random perturbations. The linear operator is supposed to have an eigenfunction of constant sign, and we show its influence, as well as the influence of its eigenvalue and of the other parameters
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Exponential stability of impulsive fractional neutral stochastic integro-differential equations with nonlocal conditions Stochastics (IF 0.9) Pub Date : 2023-01-16 K. Dhanalakshmi, P. Balasubramaniam
This manuscript addresses the existence and exponential stability of impulsive fractional neutral stochastic integrodifferential equations (IFNSIDEs) driven by Poisson jump and fractional Brownian motion (fBm) with nonlocal conditions via the Mönch fixed point theorem. The sufficient conditions for stability results are derived based on the pth moment exponential stable with the help of new impulsive
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Convoluted fractional Poisson process of order k Stochastics (IF 0.9) Pub Date : 2023-01-16 Ayushi S. Sengar, Neelesh S. Upadhye
In this article, we define a convoluted fractional Poisson process of order k (CFPPoK), which is governed by the discrete convolution operator in the system of fractional differential equations. Next, we obtain its one-dimensional distribution by using the Laplace transform of its state probabilities. Various distributional properties, such as probability generating function, moment generating function
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On Besov regularity and local time of the solution to the stochastic heat equation Stochastics (IF 0.9) Pub Date : 2023-01-11 Brahim Boufoussi, Yassine Nachit
Sharp Besov regularities in time and space variables are investigated for (u(t,x),t∈[0,T],x∈R)(u(t,x),t∈[0,T],x∈R) , the mild solution to the stochastic heat equation driven by space–time white noise. Existence, Hölder continuity, and Besov regularity of local times are established for u(t,x) viewed either as a process in the space variable or time variable. Hausdorff dimensions of their corresponding
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Complete convergence and complete moment convergence for widely negative orthant dependent random variables under the sub-linear expectations Stochastics (IF 0.9) Pub Date : 2023-01-11 Anna Kuczmaszewska
In this work there is considered complete convergence and complete moment convergence for widely negative orthant dependent random variables under the sub-linear expectations. The presented results concern the weighted sums of these random variables and extend the corresponding results in classical probability space to the case of sub-linear expectation space.
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Solving a nonlinear fractional SPDE with spatially inhomogeneous white noise Stochastics (IF 0.9) Pub Date : 2023-01-10 Junfeng Liu
In this paper, we study the following nonlinear fractional stochastic partial differential equation ∂∂tu(t,x)=D(x,D)u(t,x)+g(u(t,x))∂2wρ∂t∂x(t,x),t≥0,x∈R,∂∂tu(t,x)=D(x,D)u(t,x)+g(u(t,x))∂2wρ∂t∂x(t,x),t≥0,x∈R, where D(x,D) denotes the Markovian generator of a stable-like Feller process with variable order and g(⋅):R→R is a measurable function. The forcing noise denoted by ∂2wρ∂t∂x(t,x) is a spatially
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Uniform asymptotics for ruin probabilities of a time-dependent bidimensional renewal risk model with dependent subexponential claims Stochastics (IF 0.9) Pub Date : 2023-01-09 Zaiming Liu, Bingzhen Geng, Xinyue Man, Xinyu Liu
This paper considers a continuous-time bidimensional renewal risk model with subexponential claims. In this model, the claim size vectors and their inter-arrival times form a sequence of independent and identically distributed random vectors following some general dependence structures introduced by [T. Jiang, Y. Wang, Y. Chen and H. Xu, Uniform asymptotic estimate for finite-time ruin probabilities
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Persistence and extinction of a modified LG-Holling type II predator-prey model with two competitive predators and Lévy jumps Stochastics (IF 0.9) Pub Date : 2023-01-08 Yongxin Gao, Fan Yang
In this paper, we study a three-species predator-prey model with modified LG-Holling type II with Lévy jumps, and we take the competition among predators into consideration. First, We use an Ornstein-Uhlenbeck process to describe the environmental stochasticity and prove that there is a unique positive solution to the system by mathematical analysis skills such as comparison theorem. Futhermore, the
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Conditioning continuous-time Markov processes by guiding Stochastics (IF 0.9) Pub Date : 2022-12-05 Marc Corstanje, Frank van der Meulen, Moritz Schauer
ABSTRACT A continuous-time Markov process X can be conditioned to be in a given state at a fixed time T>0 using Doob's h-transform. This transform requires the typically intractable transition density of X. The effect of the h-transform can be described as introducing a guiding force on the process. Replacing this force with an approximation defines the wider class of guided processes. For certain
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Existence and upper semicontinuity of random attractors for the 2D stochastic convective Brinkman–Forchheimer equations in bounded domains Stochastics (IF 0.9) Pub Date : 2022-11-30 K. Kinra, M. T. Mohan
In this work, we discuss the large time behaviour of the solutions of two-dimensional stochastic convective Brinkman–Forchheimer (SCBF) equations on bounded domains. Under the functional setting V↪H↪V′, where H and V are appropriate separable Hilbert spaces and the fact that the embedding V↪H is compact, we establish the existence of random attractors in H for the stochastic flow generated by 2D SCBF
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Hedging portfolio for a market model of degenerate diffusions Stochastics (IF 0.9) Pub Date : 2022-11-30 Mine Çağlar, İhsan Demirel, Ali Süleyman Üstünel
We consider a semimartingale market model when the underlying diffusion has a singular volatility matrix and compute the hedging portfolio for a given payoff function. Recently, the representation problem for such degenerate diffusions as a stochastic integral with respect to a martingale has been completely settled. This representation and Malliavin calculus established further for the functionals
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Asymptotic behaviour of solutions to stochastic three-dimensional globally modified Navier–Stokes equations Stochastics (IF 0.9) Pub Date : 2022-11-27 Cung The Anh, Nguyen Van Thanh, Phan Thi Tuyet
We consider 3D stochastic globally modified Navier–Stokes equations in bounded domains with homogeneous Dirichlet boundary conditions and infinite dimensional Wiener process. We study stability properties of stationary solutions. We also show that one can stabilize an unstable stationary solution by using a multiplicative Itô noise of sufficient intensity or a linear internal feedback controller with
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Generalized weighted number operators on functionals of discrete-time normal martingales Stochastics (IF 0.9) Pub Date : 2022-11-27 Jing Zhang, Caishi Wang, Lixia Zhang, Lu Zhang
Let M be a discrete-time normal martingale that has the chaotic representation property. Then, from the space of square integrable functionals of M, one can construct generalized functionals of M. In this paper, by using a type of weights, we introduce a class of continuous linear operators acting on generalized functionals of M, which we call generalized weighted number (GWN) operators. We prove that
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Complete moment convergence for maximum of randomly weighted sums of martingale difference sequences Stochastics (IF 0.9) Pub Date : 2022-11-17 Zongfeng Qi, Jinyu Zhou, Jigao Yan
In this paper, complete moment convergence for maximum of randomly weighted sums and complete convergence for randomly indexed sums of martingale difference sequences (MDS) are investigated under some proper and sufficient conditions. A Marcinkiewicz–Zygmund type strong law of large numbers (MZSLLN) for MDS is obtained. In addition, relationships among weights, weight functions and boundary functions
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Decoherence for Markov chains Stochastics (IF 0.9) Pub Date : 2022-10-20 Francesco Fidaleo, Elia Vincenzi
It is known that the subspace generated by the eigenvectors pertaining to the peripheral spectrum of any stochastic matrix is canonically equipped with a structure of a (finite-dimensional abelian) C∗-algebra under a canonical new product introduced by E.G. Effros and M.-D. Choi. We prove that the restriction of the action of such a stochastic matrix to this subspace is indeed a ∗-automorphism. The