论文标题
对不均匀的马尔可夫跳跃过程和应用的强烈收敛均匀近似
Strongly convergent homogeneous approximations to inhomogeneous Markov jump processes and applications
论文作者
论文摘要
对时间均匀的马尔可夫跳跃过程的研究是概率理论中的一个传统话题，最近在各种应用中引起了很大的关注。但是，它们的灵活性还会产生重大的数学负担，通常使用众所周知的通用分布近似或模拟来规避。本文提供了一种新颖的近似方法，该方法量身定制了时间均匀的马尔可夫跳跃过程的动力学，以在日益精细的泊松网格上满足其时间不均匀的对应物的动力学。建立了基于Skorokhod $ J_1 $公制的过程的强烈融合，并提供了融合率。在传统的规律性假设下，为无条件代理建立了分布收敛，达到了相同的限制。特别注意目标过程具有一个吸收状态和其余瞬态的情况，吸收时间也会融合。概述了一些应用，例如单变量危险率估计，破坏概率和多元相型密度评估。
The study of time-inhomogeneous Markov jump processes is a traditional topic within probability theory that has recently attracted substantial attention in various applications. However, their flexibility also incurs a substantial mathematical burden which is usually circumvented by using well-known generic distributional approximations or simulations. This article provides a novel approximation method that tailors the dynamics of a time-homogeneous Markov jump process to meet those of its time-inhomogeneous counterpart on an increasingly fine Poisson grid. Strong convergence of the processes in terms of the Skorokhod $J_1$ metric is established, and convergence rates are provided. Under traditional regularity assumptions, distributional convergence is established for unconditional proxies, to the same limit. Special attention is devoted to the case where the target process has one absorbing state and the remaining ones transient, for which the absorption times also converge. Some applications are outlined, such as univariate hazard-rate density estimation, ruin probabilities, and multivariate phase-type density evaluation.
