论文标题
由分数布朗动作驱动的分布依赖性SDE的渐近行为
Asymptotic behaviors for distribution dependent SDEs driven by fractional Brownian motions
论文作者
论文摘要
在本文中，我们研究了一类依赖分布的随机微分方程的小型渐近行为，该方程是由hurst参数$ h \ in（1/2,1）$和幅度$ \ ep^h $ promage $ h \ in（1/2,1）驱动的。通过在派系布朗运动设置中建立一个变分框架和两个弱收敛标准，我们为此方程建立了大而中等的偏差原理。此外，我们还获得了中心极限定理，其中极限过程求解了涉及漂移系数的狮子衍生物的线性方程。
In this paper, we study small-time asymptotic behaviors for a class of distribution dependent stochastic differential equations driven by fractional Brownian motions with Hurst parameter $H\in(1/2,1)$ and magnitude $\ep^H$. By building up a variational framework and two weak convergence criteria in the factional Brownian motion setting, we establish the large and moderate deviation principles for this type equations. Besides, we also obtain the central limit theorem, in which the limit process solves a linear equation involving the Lions derivative of the drift coefficient.
