任意随机序列关于非齐次马氏链的随机和的一类随机偏差定理

In this paper, the notion of limit random logarithmic likelihood ratio of stochastic sequence, as a measure of dissimilarity between the joint distribution on measure P and the Markov distribution on measure Q, is introduced. A class of random approximation theorems for arbitrary stochastic dominated sequence are obtained by using the tools of generating functions and the tailed-probability generating functions.     

平面上Volterra型随机微分方程解的轨道惟一性

In this paper we prove the pathwise uniqueness of a kind of two-parameter Volterra type stochastic differential equations under the coefficients satisfy the nonLipschitz conditions. We use a martingale formula in stead of Itǒ formula, which leads to simplicity the process of proof and extends the result to unbounded coefficients case.     

Stochastic flows of mappings

In this paper,the stochastic flow of mappings generated by a Feller convolution semigroup on a compact metric space is studied.This kind of flow is the generalization of superprocesses of stochastic flows and stochastic diffeomorphism induced by the strong solutions of stochastic differential equations.     

Asymptotic behavior of impulsive stochastic functional differential equations

In this paper, a nonlinear and nonautonomous impulsive stochastic functional differential equation is considered. By establishing a nonautonomous -operator impulsive delay inequality and using the properties of ρ-cone and stochastic analysis technique, we obtain the p-attracting set and p-invariant set of the impulsive stochastic functional differential equation. An example is also discussed to illustrate the efficiency of the obtained results.     

Output Feedback H∞ Control for a Class of Nonlinear Stochastic Systems

This paper deals with the output feedback H∞ control problem for a class of nonlinear stochastic systems. Based on the latest developed theory of stochastic dissipation, a notable result about the nonlinear H∞ output feedback control of deterministic system is generalized to the stochastic case. Finally, in the cases of state feedback and output feedback, two families of controllers are provided respectively.     

Strong solution of Itô type set-valued stochastic differential equation

In this paper, we shall firstly illustrate why we should introduce an It5 type set-valued stochastic differential equation and why we should notice the almost everywhere problem. Secondly we shall give a clear definition of Aumann type Lebesgue integral and prove the measurability of the Lebesgue integral of set-valued stochastic processes with respect to time t. Then we shall present some new properties, especially prove an important inequality of set-valued Lebesgue integrals. Finally we shall prove the existence and the uniqueness of a strong solution to the It5 type set-valued stochastic differential equation.     

STABILITY IN LAGRANGE SENSE FOR A CLASS OF STOCHASTIC STATIC NEURAL NETWORKS WITH MIXED TIME DELAYS

In this paper, the stability in Lagrange sense of a class of stochastic static neural networks with mixed time delays is studied. Based on the Lyapunov stability theory and with the help of stochastic analysis technique, the criteria for the stability in Lagrange sense of stochastic static neural networks with mixed time delays is obtained. One example is given to verify the advantage and applicability of the proposed results.     

The high-order SPDEs driven by multi-parameter fractional noises

The existence and uniqueness of the solutions are proved for a class of fourth-order stochastic heat equations driven by multi-parameter fractional noises. Furthermore the regularity of the solutions is studied for the stochastic equations and the existence of the density of the law of the solution is obtained.     

Square-mean almost periodic solutions to some stochastic evolution equations

This paper concerns the square-mean almost periodic mild solutions to a class of abstract nonautonomous functional integro-differential stochastic evolution equations in a real separable Hilbert space. By using the so-called "Acquistapace–Terreni" conditions and the Banach fixed point theorem, we establish the existence, uniqueness and the asymptotical stability of square-mean almost periodic solutions to such nonautonomous stochastic differential equations. As an application, almost periodic solution to a concrete nonautonomous stochastic integro-differential equation is considered to illustrate the applicability of our abstract results.     

随机流的超过程的状态分解

In this paper, we reconstruct the superprocesses of stochastic flows by martingale method, and prove that if and only if the infinitesimal particles never hit each other, then atomic part and diffuse part of this kind of superprocesses will be also superprocesses of stochastic flows. This result completely answers the open problem in [1].     

关于任意离散随机序列的一个强偏差定理

引用极限对数似然比的概念作为任意随机序列联合分布与其边缘分布"不相似性"的度量,构造几乎处处收敛的上鞅,讨论了任意离散随机序列的强偏差定理.     

Stochastic logistic equation with infinite delay

This paper perturbs the famous logistic equation with infinite delay into the corresponding stochastic system This study shows that the above stochastic system has a global positive solution with probability 1 and gives the asymptotic pathwise estimation of this solution. In addition, the superior limit of the average in time of the sample path of the solution is estimated. This work also establishes the sufficient conditions for extinction, nonpersistence in the mean, and weak persistence of the solution. The critical value between weak persistence and extinction is obtained. Then these results are extended to n‐dimensional stochastic Lotka–Volterra competitive system with infinite delay. Finally, this paper provides some numerical figures to illustrate the results. The results reveal that, firstly, different types of environmental noises have different effects on the persistence and extinction of the population system; secondly, the delay has no effect on the persistence and extinction of the stochastic system.Copyright © 2012 John Wiley & Sons, Ltd.     

On intensities of perturbed random measures on Hausdorff spaces

Abstract

This article studies classes of random measures on topological spaces perturbed by stochastic processes (a.k.a. modulated random measures). We render a rigorous construction of the stochastic integral of functions of two variables and showed that such an integral is a random measure. We establish a new Campbell-type formula that, along with a rigorous construction of modulation, leads to the intensity of a modulated random measure. Mathematical formalism of integral-driven random measures and their stochastic intensities find numerous applications in stochastic models, physics, astrophysics, and finance that we discuss throughout the article.     

An ornstein-uhlenbeck model for random oscillations

We consider the effect of a random "noise" on an n-dimensional simple harmonic oscillator with time-dependent damping. The noise in the system is modelled by incorporating a Brownian motion term in the equation for the velocity process of the simple harmonic oscillator, giving a stochastic differential equation similar to that of an Ornstein-Uhlenbeck proces. Necessary and sufficient conditions for the convergence of the solution of this SDE to an orbit of simple harmonic motion (satisfying the usual ODE) are then obtained     

Uniqueness of diffusion generators for two types of particle systems with singular interactions

For two types of stochastic particle systems in we show non-explosion in finite time by proving that their respective generators are L¹(μ)-unique, where μ is their respective invariant (in these cases even symmetrizing) measure. We also prove the much harder L²(μ)-uniqueness in both models.     

Tribute to Endre Csáki and Pál Révész

Summary This article provides a glimpse of some of the highlights of the joint work of Endre Csáki and Pál Révész since 1979. The topics of this short exploration of the rich stochastic milieu of this inspiring collaboration revolve around Brownian motion, random walks and their long excursions, local times and additive functionals, iterated processes, almost sure local and global central limit theorems, integral functionals of geometric stochastic processes, favourite sites--favourite values and jump sizes for random walk and Brownian motion, random walking in a random scenery, and large void zones and occupation times for coalescing random walks.     

On the Lattice Approximation for Certain Generalized Vector Markov Fields in Four Spacetime Dimensions

We extend previous results by Albeverio, Iwata and Schmidt on the construction of a convergent lattice approximation for invariant scalar 3-vector generalized random fields F of an infinitely divisible type and apply them to the construction of convergent lattice approximation for the generalized random vector field A determined by the stochastic quaternionic Cauchy–Riemann equation A = F.     

Continuous Singularity of the Weak Limit of Convolution Powers of a Discrete Probability Measure on 2 × 2 Stochastic Matrices

Let be a probability measure on n 2 × 2 stochastic matrices, n an arbitrary positive integer, and = (w) lim _n ⁿ , such that the support of consists of 2 × 2 stochastic matrices of rank one, and as such, can be regarded as a probability measure on [0, 1]. We present simple sufficient conditions for to be continuous singular w.r.t. the Lebesgue measure on [0, 1]. We also determine , given .     

Sample-Path Stability of Non-Stationary Dynamic Economic Systems

The goal of this paper is to introduce and illustrate a new approach to the stability analysis of sample-paths of non-linear stochastic economic models with non-stationary components. We place our study within the mathematical theory of random dynamical systems and apply the concept of a random fixed point which is tailor-made for the study of the long-term behavior of sample-paths in stochastic systems. The main tool for the application of this approach is a Banach-type fixed point theorem for non-stationary random dynamical systems which is proved here. The concept and the theorem are thoroughly explained and illustrated by examples from stochastic growth theory.     

关于任意非负随机序列随机和的一类随机偏差定理

本文引入任意随机变量序列随机极限对数似然比概念,作为任意相依随机序列联合分布与其边缘乘积分布“不相似”性的一种度量,利用构造新的密度函数方法来建立几乎处处收敛的上鞅,在适当的条件下,给出了任意受控随机序列的一类随机偏差定理.