Random attractors for stochastic differential equations driven by two-sided Levy processes
Random attractors for stochastic differential equations driven by two-sided Levy processes
复制标题
两侧 Lévy 过程驱动的随机微分方程的随机吸引子
DOI：
10.1080/07362994.2019.1637264
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发表时间：
2019
影响因子：
1.3
通讯作者：
Pei Bin
中科院分区：
文献类型：
--
作者：
Zhang Xiaoyu;Xu Yong;Schmalfuss Bjoern;Pei Bin
本文研究了一类具有乘性双边Lévy噪声的非线性Marcus随机微分方程解的渐近性。我们计划把这个方程看作一个随机动力系统。因此，我们必须将L噪声解释为一个双边度规动力系统。为此，我们必须介绍这种噪声的一些基本性质。到目前为止，大多数研究只讨论了由两个独立的Lévy过程组合而成的双边Lévy过程。本文通过扩展概率空间，给出了双边L过程的另一种定义。有了这个度规动力系统，我们将证明具有特定漂移系数和乘性噪声的Marcus随机微分方程产生一个具有随机吸引子的随机动力系统。
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.