关于具有流之间随机切换的分段确定性 Markov 过程相关不变测度的绝对连续性
On absolute continuity of invariant measures associated with a piecewise-deterministic Markov processes with random switching between flows
AI总结：
本文研究了生物模型中分段确定性 Markov 过程平稳分布的绝对连续性，该过程由 Poisson 过程跳跃和连续半流切换组成，提出了一组可验证条件，证明其不变分布具有关于 Lebesgue 测度的密度。
摘要：
我们关注生物模型中常见的分段确定性 Markov 过程平稳分布的绝对连续性。该过程包含确定性运动和随机跳跃，跳跃发生在 Poisson 过程的跳跃时刻。跳跃后的位置由跳跃前状态的随机变换得到。跳跃间，运动由连续半流控制，半流在跳跃后直接切换。本文的主要目标是给出一组可验证的条件，表明该过程对应于其跳跃后位置构成的 Markov 链的遍历不变测度的任何不变分布，均具有关于 Lebesgue 测度的密度。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
