无耗散时滞随机微分方程的平稳分布
Stationary Distributions for Retarded Stochastic Differential Equations without Dissipativity
摘要：
时滞随机微分方程（SDEs）是一类广泛存在于实际生活中的系统。大多数现有的结果，使耗散条件的关键使用。对于漂移和扩散系数都只依赖于时滞变元的“纯时滞”系统，已有的结果不再适用。这项工作使用的变分常数公式，以克服困难，由于缺乏在目前的时间信息。本文建立了不需要满足耗散条件的时滞随机微分方程平稳分布的存在唯一性。本文所考虑的时滞随机微分方程还包括中立型随机微分方程和由Lévy过程驱动的可能不允许有限二阶矩的随机微分方程。
英文摘要：
Retarded stochastic differential equations (SDEs) constitute a large collection of systems arising in various real-life applications. Most of the existing results make crucial use of dissipative conditions. Dealing with "pure delay" systems in which both the drift and the diffusion coefficients depend only on the arguments with delays, the existing results become not applicable. This work uses a variation-of-constants formula to overcome the difficulties due to the lack of the information at the current time. This paper establishes existence and uniqueness of stationary distributions for retarded SDEs that need not satisfy dissipative conditions. The retarded SDEs considered in this paper also cover SDEs of neutral type and SDEs driven by Lévy processes that might not admit finite second moments.
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