论文标题
续签过程的职业时间与离散马尔可夫链结合
Occupation time of a renewal process coupled to a discrete Markov chain
论文作者
论文摘要
半马尔可夫过程是根据马尔可夫链改变状态的过程，但在变化之间需要随机的时间。我们考虑对两国马尔可夫进程的职业时间的经典Lamperti定律的半马尔可夫过程的概括。我们在拉普拉斯空间中提供了明确的表达，以在过程的各个状态下分布职业时间的任意线性组合。我们讨论了该结果的几个后果。特别是，我们推断出该数量的限制分布在长期缩放制度中按时间重新缩放，以及有限的时间校正。
A semi-Markov process is one that changes states in accordance with a Markov chain but takes a random amount of time between changes. We consider the generalisation to semi-Markov processes of the classical Lamperti law for the occupation time of a two-state Markov process. We provide an explicit expression in Laplace space for the distribution of an arbitrary linear combination of the occupation times in the various states of the process. We discuss several consequences of this result. In particular, we infer the limiting distribution of this quantity rescaled by time in the long-time scaling regime, as well as the finite-time corrections to its moments.
