论文标题
由布朗运动驱动的多尺度系统的中等偏差原理
Moderate deviation principle for multiscale systems driven by fractional Brownian motion
论文作者
论文摘要
在本文中，我们研究了慢速随机动力学系统的中等偏差原理（MDP），在该系统中，慢动作由小的分数布朗运动（FBM）控制，并带有Hurst参数$ h \ in（1/2,1）$。我们在MDP所持的中等偏差缩放和Hurst参数$ H $上得出条件。此外，我们表明，在典型情况下，$ h = 1/2 $的$ H $中所产生的动作功能是不连续的，这表明FBM扰动的随机动力学系统的尾巴行为与标准Brownian Motion扰动的此类系统的尾巴行为不同。
In this paper we study the moderate deviations principle (MDP) for slow-fast stochastic dynamical systems where the slow motion is governed by small fractional Brownian motion (fBm) with Hurst parameter $H\in(1/2,1)$. We derive conditions on the moderate deviations scaling and on the Hurst parameter $H$ under which the MDP holds. In addition, we show that in typical situations the resulting action functional is discontinuous in $H$ at $H=1/2$, suggesting that the tail behavior of stochastic dynamical systems perturbed by fBm can have different characteristics than the tail behavior of such systems that are perturbed by standard Brownian motion.
