带小扰动的随机发展方程的不变测度

本文考虑带小扰动的随机发展方程,证明如何建立此方程的耦合解.作为应用,我们证明解的Feller连续性和不变测度的存在唯一性.还进一步建立了当扰动趋于零时,关于这族不变测度的大偏差原理.     

平移不变的随机串测度

利用围道估计的方法，刻划在相变点处的平移不变随机串测度，证明了：对二维以上情况，当口充分大时，在临界点处，平移不变随机串测度有且只有两个极点，也即任一平移不变随机串测度都是这两个极点的凸组合．     

非均匀介质中波动方程的部分不变解

讨论了来自于非均匀介质中波动方程的部分不变解的存在性，证明了在波速满足适当的条件下部分不变解是存在的，并得到了部分不变解。     

跳过程的不变测度与q对的不变测度

本文讨论了一般状态空间上具有不变测度的q对的对偶q对的构造问题,证明了正则q对的不变测度是它的相应跳过程的不变测度的充要条件是该q对的对偶q对是正则的。     

一维粘弹性波动方程弹性系数的识别方法

本文就一维粘弹性波动方程弹性系数的求解问题，给出了一个新的求解方法．通过对算法进行分析可知，该方法具有较小的计算量，并且具较好的数值稳定性．数值模拟表明了该方法的可行性及有效性．     

一类非自治分数阶随机波动方程的随机吸引子

本文考虑带加性噪声的非自治分数阶随机波动方程在无界区域R~n上的渐近行为.首先将随机偏微分方程转化为随机方程,其解产生一个随机动力系统,然后运用分解技术建立该系统的渐近紧性,最后证明随机吸引子的存在性.     

对称稳定过程的不变测度

对R~d(d≥1)中指标a,0相似文献   

Q过程的μ不变测度

设Q={qij;i,j∈E}是可数集E上的全稳定Q-矩阵，或单瞬时不可和准保守拟Q-矩阵，m={mj;j∈E}是Q的有限μ不变测度，则一定存在Q过程P（t)，使m是P（t)的μ不变测度。     

非线性粘弹性波动方程的非协调混合元超收敛分析和外推

研究了非线性粘弹性波动方程在新混合元格式下非协调混合有限元方法.利用插值理论、高精度分析、平均值理论和对时间t的导数转移的技巧,借助于EQ_1~(rot)元所具有的两个性质:(a)其相容误差为O(h~2)阶比它的插值误差高一阶;(b)插值算子与Ritz投影等价,以及插值后处理技术,分别导出了原始变量u的H~1模和中间变量p的L~2模下O(h~2)阶超逼近性质和整体超收敛.进一步,通过构造适当的辅助问题,运用Richordson外推格式,得到了更高精度O(h~3)阶外推结果.     

非Lipschitz系数随机波动方程适度解的存在唯一性

本文在系数为非Lipschitz条件下(Lipschitz和线性增长作为其特例),通过构造逐次逼近列的方法证明了随机波动方程适度解的存在唯一性.     

On the Uniqueness of Invariant Measure of the Burgers Equation Driven by Lévy Processes

In this paper, we prove the uniqueness of the invariant measure for one-dimensional Burgers equations perturbed by Lévy processes with Dirichlet boundary conditions. The work was supported by the Natural Science Foundation of China and 973 Project.     

Elementary bifurcations for a simple dynamical system under non-Gaussian Lévy noises

Nonlinear dynamical systems are sometimes under the influence of random fluctuations. It is desirable to examine possible bifurcations for stochastic dynamical systems when a parameter varies.     

Stochastic PDIEs and backward doubly stochastic differential equations driven by Lévy processes

In this paper, a new class of backward doubly stochastic differential equations driven by Teugels martingales associated with a Lévy process satisfying some moment condition and an independent Brownian motion is investigated. We obtain the existence and uniqueness of solutions to these equations. A probabilistic interpretation for solutions to a class of stochastic partial differential integral equations is given.     

Space Semi-Discretisations for a Stochastic Wave Equation

We study an approximation scheme for a nonlinear stochastic wave equation in one-dimensional space, driven by a spacetime white noise. The sequence of approximations is obtained by discretisation of the Laplacian operator. We prove L ^p -convergence to the solution of the equation and determine the rate of convergence. As a corollary, almost sure convergence, uniformly in time and space, is also obtained. Finally, the speed of convergence is tested numerically.⋆Supported by the grant BMF 2003-01345 from the Dirección General de Investigación, Ministerio de Ciencia y Tecnología, Spain.     

Doubly reflected BSDEs driven by a Lévy process

In this paper, we show the existence and uniqueness of the solution for a class of doubly reflected backward stochastic differential equations driven by a Lévy process (DRBSDELs in short) by means of the penalization method as well as the fixed point theorem. In addition, we obtain the comparison theorem for the solutions of DRBSDELs. As an application, we give a probabilistic formula for the viscosity solution of a class of partial differential-integral equations (PDIEs in short) with two obstacles.     

Stochastic PDIEs with nonlinear Neumann boundary conditions and generalized backward doubly stochastic differential equations driven by Lévy processes

In this paper, a new class of generalized backward doubly stochastic differential equations (GBDSDEs in short) driven by Teugels martingales associated with Lévy process and the integral with respect to an adapted continuous increasing process is investigated. We obtain the existence and uniqueness of solutions to these equations. A probabilistic interpretation for solutions to a class of stochastic partial differential integral equations (PDIEs in short) with a nonlinear Neumann boundary condition is given.     

One-dimensional stochastic Burgers equation driven by Lévy processes

In this paper, we proved the global existence and uniqueness of the strong, weak and mild solutions for one-dimensional Burgers equation perturbed by a Poisson form process, a Poisson form and Q-Wiener process with the Dirichlet bounded condition. We also proved the existence of the invariant measure of these models.     

Delay differential equations driven by Lévy processes: Stationarity and Feller properties

We consider a stochastic delay differential equation driven by a general Lévy process. Both the drift and the noise term may depend on the past, but only the drift term is assumed to be linear. We show that the segment process is eventually Feller, but in general not eventually strong Feller on the Skorokhod space. The existence of an invariant measure is shown by proving tightness of the segments using semimartingale characteristics and the Krylov–Bogoliubov method. A counterexample shows that the stationary solution in completely general situations may not be unique, but in more specific cases uniqueness is established.     

A note on the reflected backward stochastic differential equations driven by a Lévy process with stochastic Lipschitz condition

In this note, we prove the existence and uniqueness of the solution for a class of reflected backward stochastic differential equations (RBSDEs in short) related to the subdifferential operator of a lower semi-continuous convex function, driven by Teugels martingales associated with a Lévy process. Some known results are generalized and improved.