论文标题
关于与分段确定的马尔可夫进程相关的不变措施的绝对连续性，在流之间随机切换
On absolute continuity of invariant measures associated with a piecewise-deterministic Markov processes with random switching between flows
论文作者
论文摘要
我们关注的是与某些分段确定性马尔可夫过程相对应的固定分布的绝对连续性，该过程通常在生物模型中遇到。所研究的过程涉及在泊松过程的跳跃时间发生的随机跳动的确定性运动。跳跃后的位置是通过跳跃前状态的随机转化获得的。在跳跃之间，运动由连续的半流动控制，后者在跳跃后直接切换。本文的主要目的是提供一组可验证的条件，这意味着所考虑的过程的任何不变分布与马尔可夫链的千古不变的度量相对应，该措施由其后的临时位置给出的马尔可夫链，相对于Lebesgue度量，其密度具有密度。
We are concerned with the absolute continuity of stationary distributions corresponding to some piecewise deterministic Markov process, being typically encountered in biological models. The process under investigation involves a deterministic motion punctuated by random jumps, occurring at the jump times of a Poisson process. The post-jump locations are obtained via random transformations of the pre-jump states. Between the jumps, the motion is governed by continuous semiflows , which are switched directly after the jumps. The main goal of this paper is to provide a set of verifiable conditions implying that any invariant distribution of the process under consideration that corresponds to an ergodic invariant measure of the Markov chain given by its post-jump locations has a density with respect to the Lebesgue measure.
