扩散-嬗变耦合动力系统的大偏差原理
Large deviation principle for dynamical systems coupled with diffusion-transmutation processes
摘要：
在本文中，我们介绍了一个数学仪器，这是相关的理解一个动力系统与小的随机扰动和耦合的所谓的嬗变过程-后者从一个模式跳到另一个，从而修改系统的动态。特别是，我们研究了退出问题，即，给出了相应过程退出给定有界开域的退出概率的渐近估计，并形式化地证明了当随机扰动为零时，退出位置与类型占有时间联合的大偏差原理.此外，在一定的条件下，出口的地方和类型的分布在出口时间的确定，作为一个后果，这方面的信息也给出了限制相关的偏微分方程系统的小参数为零的狄利克雷问题。
英文摘要：
In this paper, we introduce a mathematical apparatus that is relevant for understanding a dynamical system with small random perturbations and coupled with the so-called transmutation process -- where the latter jumps from one mode to another, and thus modifying the dynamics of the system. In particular, we study the exit problem, i.e., an asymptotic estimate for the exit probabilities with which the corresponding processes exit from a given bounded open domain, and then formally prove a large deviation principle for the exit position joint with the type occupation times as the random perturbation vanishes. Moreover, under certain conditions, the exit place and the type of distribution at the exit time are determined and, as a consequence of this, such information also give the limit of the Dirichlet problems for the associated partial differential equation systems with a vanishing small parameter.
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