论文标题
分段确定的马尔可夫进程的子类的有界lipschitz距离中的指数性千差万别，在流之间随机切换
Exponential ergodicity in the bounded-Lipschitz distance for a subclass of piecewise-deterministic Markov processes with random switching between flows
论文作者
论文摘要
在本文中，我们研究了具有波兰状态空间的分段确定性马尔可夫过程的子类，涉及确定性运动，该运动是在指数分布的时间间隔下发生的随机跳动的确定性运动。在这些间隔中的每个间隔中，该过程都遵循流量，在所有可能的有限集中随机选择。我们的主要目标是提供一组可验证的条件，以保证此类过程的指数性千古（就有限的Lipschitz距离而言），这仅指的是流量的属性和Markov链的过渡定律。此外，我们为这些过程的特定实例的指数性千差线建立了一个简单的标准，适用于某些生物学模型，其中跳跃是由具有位置依赖性概率的迭代功能系统的作用而产生的。
In this paper, we study a subclass of piecewise-deterministic Markov processes with a Polish state space, involving deterministic motion punctuated by random jumps that occur at exponentially distributed time intervals. Over each of these intervals, the process follows a flow, selected randomly among a finite set of all possible ones. Our main goal is to provide a set of verifiable conditions guaranteeing the exponential ergodicity for such processes (in terms of the bounded Lipschitz distance), which would refer only to properties of the flows and the transition law of the Markov chain given by the post-jump locations. Moreover, we establish a simple criterion on the exponential ergodicity for a particular instance of these processes, applicable to certain biological models, where the jumps result from the action of an iterated function system with place-dependent probabilities.
