Ji, Lina Zheng, Xiangqi
Published in
Acta Mathematica Scientia

For continuous-state branching processes in Lévy random environments, the recursion of n-moments and the equivalent condition for the existence of general f-moments are established, where f is a positive continuous function satisfying some standard conditions.

Jiang, Yiming Wang, Suxin Wang, Xingchun
Published in
Acta Mathematica Scientia

In this article, we consider the long time behavior of the solutions to stochastic wave equations driven by a non-Gaussian Lévy process. We shall prove that under some appropriate conditions, the exponential stability of the solutions holds. Finally, we give two examples to illustrate our results.

Xiong, Jie Yang, Xu
Published in
Acta Mathematica Scientia

This is a survey on the strong uniqueness of the solutions to stochastic partial differential equations (SPDEs) related to two measure-valued processes: superprocess and Fleming-Viot process which are given as rescaling limits of population biology models. We summarize recent results for Konno-Shiga-Reimers’ and Mytnik’s SPDEs, and their related di...

Chen, Yong Liu, Yong
Published in
Acta Mathematica Scientia

In this article, some properties of complex Wiener-Itô multiple integrals and complex Ornstein-Uhlenbeck operators and semigroups are obtained. Those include Stroock’s formula, Hu-Meyer formula, Clark-Ocone formula, and the hypercontractivity of complex Ornstein-Uhlenbeck semigroups. As an application, several expansions of the fourth moments of co...

Li, Heyu Chen, Xia
Published in
Acta Mathematica Scientia

This article establishes the precise asymptotics Eum(t,x)(t→>∞orm→∞)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb{E}u^m(t,x)\;\;\;\;(t\rightarrow\infty\;{\rm{...

Garzón, Johanna Tindel, Samy Torres, Soledad
Published in
Acta Mathematica Scientia

In this note, we study a discrete time approximation for the solution of a class of delayed stochastic differential equations driven by a fractional Brownian motion with Hurst parameter H ∈ (1/2,1). In order to prove convergence, we use rough paths techniques. Theoretical bounds are established and numerical simulations are displayed.

Sylla, Lamine
Published in
Acta Mathematica Scientia

We consider the problem of viscosity solution of integro-partial differential equation(IPDE in short) with one obstacle via the solution of reflected backward stochastic differential equations(RBSDE in short) with jumps. We show the existence and uniqueness of a continuous viscosity solution of equation with non local terms, if the generator is not...

Hu, Yaozhong Lê, Khoa
Published in
Acta Mathematica Scientia

We obtain the Holder continuity and joint Hölder continuity in space and time for the random field solution to the parabolic Anderson equation (∂t−12Δ)u=u⋄W˙\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\odd...

Balan, Raluca M Quer-Sardanyons, Lluís Song, Jian
Published in
Acta Mathematica Scientia

In this article, we consider the Parabolic Anderson Model with constant initial condition, driven by a space-time homogeneous Gaussian noise, with general covariance function in time and spatial spectral measure satisfying Dalang’s condition. First, we prove that the solution (in the Skorohod sense) exists and is continuous in Lp (Ω). Then, we show...

Qiu, Jinniao Wei, Wenning
Published in
Acta Mathematica Scientia

This article is devoted to the study of fully nonlinear stochastic Hamilton-Jacobi (HJ) equations for the optimal stochastic control problem of ordinary differential equations with random coefficients. Under the standard Lipschitz continuity assumptions on the coefficients, the value function is proved to be the unique viscosity solution of the ass...