论文标题
部分可观测时空混沌系统的无模型预测
Large deviations of slow-fast systems driven by fractional Brownian motion
论文作者
论文摘要
我们考虑了一个随机微分方程的多尺度系统，其中缓慢的组件被小的小部分运动带有赫斯特索引$ h> 1/2 $，而快速组件则由独立的布朗尼运动驱动。在年轻整合框架中工作，我们使用分数演算和弱收敛参数的工具在同质化极限中建立一个较大的偏差原理，因为噪声强度和时间尺度的分离参数以适当的速度消失。我们的方法基于研究相关受控系统的限制行为。我们表明，在某些情况下，非本地率函数允许明确的非变化形式。后者允许我们对情况进行比较$ h = 1/2 $，这与经典的Freidlin-Wentzell理论相对应。此外，我们将利率函数的渐近学研究为$ h \ rightarrow {1/2}^+$，并表明它不连续$ h = 1/2。
We consider a multiscale system of stochastic differential equations in which the slow component is perturbed by a small fractional Brownian motion with Hurst index $H>1/2$ and the fast component is driven by an independent Brownian motion. Working in the framework of Young integration, we use tools from fractional calculus and weak convergence arguments to establish a Large Deviation Principle in the homogenized limit, as the noise intensity and time-scale separation parameters vanish at an appropriate rate. Our approach is based in the study of the limiting behavior of an associated controlled system. We show that, in certain cases, the non-local rate function admits an explicit non-variational form. The latter allows us to draw comparisons to the case $H=1/2$ which corresponds to the classical Freidlin-Wentzell theory. Moreover, we study the asymptotics of the rate function as $H\rightarrow{1/2}^+$ and show that it is discontinuous at $H=1/2.$
