一类带跳平均场泛函随机微分方程的平稳分布

Stationary distribution of mean-field stochastic functional differential equations with jumps

平均场方法是用来研究复杂系统的重要工具,广泛应用于各个研究领域.自Buckdahn等人提出平均场倒向随机微分方程以来,平均场方法在随机分析的应用受到了越来越多学者的关注.本文研究一类L′evy过程驱动的平均场泛函随机微分方程,基于依分布收敛的思想,对其平稳分布进行分析,得到平稳分布存在唯一性的充分条件.

The mean-field theory is a useful tool for studying large and complex systems, and it is extensively applied to several kinds of research areas. The mean-field method is becoming more and more popular in stochastic analysis since Buckdahn et al. introduced the mean-field stochastic differential equations to study backward stochastic differential equations. In this paper, we concentrate on mean-field stochastic functional differential equations driven by Levy process. The stationary distribution of the model is analyzed, and sufficient conditions for existence and uniqueness of stationary distribution is given.