随机反应扩散方程的L~P-随机吸引子

研究了定义在无界区域上具可乘白噪音的随机反应扩散方程的渐近行为.运用一致估计得到了U3-随机吸收集;对方程的解运用渐近优先估计法,建立了相应随机动力系统的渐近紧性,证明了LP-随机吸引子的存在性.该随机吸引子是紧不变集并按LP-范数吸L2中所有缓增集,其中,非线性项/满足p-1(p≥2)阶增长条件.     

一类随机种群方程解的存在性和指数稳定性

首先对一类半线性随机发展方程建立其解的存在性和渐近行为的结果,这类方程的线性部分生成一强连续半群.然后将抽象结果应用于依赖年龄的随机种群方程,获得它的存在性和渐近性质.     

一类随机种群方程解的存在性和指数稳定性

首先对一类半线性随机发展方程建立其解的存在性和渐近行为的结果,这类方程的线性部分生成一强连续半群.然后将抽象结果应用于依赖年龄的随机种群方程,获得它的存在性和渐近性质.     

随机中立型泛函微分方程的稳定性态

给出了一类中立型随机泛函方程的随机一致稳定性的充分条件,利用了新的分析技巧处理中立型时滞项,得到了中立型随机时滞泛函微分方程渐近稳定性的充分判据.在处理各种渐近估计是有效的.     

随机非经典扩散方程的Wong-Zakai逼近

研究了非自治随机非经典扩散方程的Wong-Zakai逼近在有界域上的动力学行为.方程中的两个非线性项在一定的假设下得到了方程解的一致估计,并利用正交谱分解的方法证明了方程的解在H₀¹(O)空间中的渐近紧性,由此证明了在Wong-Z akai逼近下该方程生成的非自治随机动力系统存在唯一的随机拉回吸引子.     

随机扰动下的非自治种群的随机持久性(英文)

本文考虑非线性随机扰动下的生态种群的问题.首先给出全局正解的存在性.其次,在合理的条件下讨论随机最终有界和随机持久问题,同时也给出解的渐近估计.     

随机环境中随机指标分枝过程矩的渐近性

引入了随机环境中随机指标分枝过程模型,证明了该模型矩的渐近性。     

无穷维随机微分方程的渐近概周期解

该文引入了渐近θ-概周期随机过程的概念,并在算子半群理论框架下研究了一类带有渐近概周期系数的无穷维随机微分方程,利用随机分析理论建立了此类随机微分方程渐近θ-概周期解的存在性.此外该文还引入了依路径分布渐近概周期过程的概念,并证明了上述渐近θ-概周期解还是依路径分布渐近概周期的.值得注意的是,在早期的研究结果中,建立的均是更弱的一维分布渐近概周期解的存在性.     

一维弱噪声随机Burgers方程的奇摄动解

讨论了一类有界区域上具有有色噪声干扰的随机Burgers方程奇摄动解,其波动率服从弱噪声Ornstein-Uhlenbeck(O-U)过程.由波运动的转移概率密度函数满足的后向Kolmogorov方程,得到随机Burgers的期望所满足的后向Kolmogorov方程.由于期望满足的后向Kolmogorov方程的初边值问题条件涉及到一类确定性Burgers方程的解,因此该问题实际上是Burgers方程和Kolmogorov方程的联立形式.首先,应用奇摄动方法,对一类确定性Burgers方程进行了正则渐近展开,由Schauder估计、Ascoli-Arzela定理证明了非线性抛物方程渐近解的有界性与存在性,由Lax-Milgram定理证明了线性抛物方程渐近解的有界性与存在性,得到波速率的形式渐近解.其次,由奇摄动理论,对期望满足的方程进行了奇摄动渐近展开和边界层矫正,由二阶线性偏微分方程理论,得到边界层函数渐近解存在且有界.应用极值原理、De-Giorgi迭代技术分别证明了波速率和波期望渐近解的余项有界,得到渐近解的一致有效性.     

随机收缩偶,随机收缩与随机算子方程的解

本文引入随机收缩偶,讨论具有随机定义域的随机集值(单值)算子方程公共随机解的存在性,建立随机收缩理论与公共随机不动点理论的联系,统一和推广了这两个方向的主要结果。 关健词:随机算子;方程;公共不动点。     

Random attractors for stochastic differential equations driven by two-sided Lévy processes

Abstract

In this paper, the asymptotic behavior of solutions for a nonlinear Marcus stochastic differential equation with multiplicative two-sided Lévy noise is studied. We plan to consider this equation as a random dynamical system. Thus, we have to interpret a Lévy noise as a two-sided metric dynamical system. For that, we have to introduce some fundamental properties of such a noise. So far most studies have only discussed two-sided Lévy processes which are defined by combining two-independent Lévy processes. In this paper, we use another definition of two-sided Lévy process by expanding the probability space. Having this metric dynamical system we will show that the Marcus stochastic differential equation with a particular drift coefficient and multiplicative noise generates a random dynamical system which has a random attractor.     

Random attractor and upper semi-continuity for Zakharov lattice system with multiplicative white noise

In this paper, we study the long-term asymptotic behaviour of solutions to the stochastic Zakharov lattice equation with multiplicative white noise. We first transfer the stochastic lattice equation into a random lattice equation and prove the existence and uniqueness of solutions which generate a random dynamical system. Then we consider the existence of a tempered random bounded absorbing set and a random attractor for the system. Finally we establish the upper semi-continuity of random attractor to the global attractor of the limiting system as the coefficients of the white noise terms tend to zero.     

The attractor of the stochastic generalized Ginzburg-Landau equation

The stochastic generalized Ginzburg-Landau equation with additive noise can be solved pathwise and the unique solution generates a random system.Then we prove the random system possesses a global random attractor in H_0~1.     

ASYMPTOTIC BEHAVIOR FOR GENERALIZED GINZBURG-LANDAU POPULATION EQUATION WITH STOCHASTIC PERTURBATION

In this paper, we are devoted to the asymptotic behavior for a nonlinear parabolic type equation of higher order with additive white noise. We focus on the Ginzburg-Landau population equation perturbed with additive noise. Firstly, we show that the stochastic Ginzburg-Landau equation with additive noise can be recast as a random dynamical system. And then, it is proved that under some growth conditions on the nonlinear term, this stochastic equation has a compact random attractor, which has a finite Hausdorff dimension.     

随机耗散Camassa-Holm方程的吸引子

可以接轨道得到带白噪声的随机耗散Camassa-Holm方程的唯—解并且可以检验该解产生随机动力系统,从而证明了该随机动力系统在H₀²中存在紧的随机吸引子.     

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     

The existence and uniqueness of<Emphasis Type="Italic">q</Emphasis>-process in random environment

We introduce some basic concepts such as random (sub-)transition function, q-function in random environment, g-process in random environment and some basic lemmas. For any continuous g-function in random environment, we prove that the g-process in random environment always exists, and that any g-process in random environment satisfies the random Kolmogorov backward equation and the minimal g-process in random environment always exists. When g is a continuous and conservative g-function in random environment, the necessary and sufficient conditions for the uniqueness of g-process in random environment are given. Finally the special cases, homogeneous random transition functions and homogeneous g-processes in random environments are considered.     

THE ANALYTICAL PROPERTIES FOR HOMOGENEOUS RANDOM TRANSITION FUNCTIONS

The concepts of Markov process in random environment and homogeneous random transition functions are introduced. The necessary and sufficient conditions for homogeneous random transition function are given. The main results in this article are the analytical properties, such as continuity, differentiability, random Kolmogorov backward equation and random Kolmogorov forward equation of homogeneous random transition functions.     

Asymptotic behavior of a system of interacting nuclear-space-valued stochastic differential equations driven by Poisson random measures

In this paper we study a system of interacting stochastic differential equations taking values in duals of nuclear spaces driven by Poisson random measures. We also consider the McKean-Vlasov equation associated with the system. We show that under suitable conditions the system has a unique solution and the sequence of its empirical distributions converges to the solution of the McKean-Vlasov equation when the size of the system tends to infinity. The results are applied to the voltage potentials of a large system of neurons and the limiting distribution of the empirical measure is obtained.This research was supported by the National Science Foundation, the Air Force Office of Scientific Research under Grant No. F49620-92-J-0154, and the Army Research Office under Grant No DAAL03-92-G-0008.     

THE CONSTRUCTION OF DENUMERABLE q-PROCESSES IN RANDOM ENVIRONMENTS SATISFYING (F) OR (B)

This article is a continuation of [9]. Based on the discussion of random Kol-mogorov forward (backward) equations, for any given q-matrix in random environment,Q(θ) = (q(θ; x, y), x, y ∈ X), an infinite class of q-processes in random environments sat-isfying the random Kolmogorov forward (backward) equation is constructed. Moreover,under some conditions, all the q-processes in random environments satisfying the random Kolmogorov forward (backward) equation are constructed.