The two-sided exit problem for an additive functional of a time-inhomogeneous Markov chain

2023/07/03 by Tomasz R. Bielecki, Bielecki, Tomasz R., Ziteng Cheng +3
Business, Management and Accounting · Mathematics · #Advanced Queuing Theory Analysis #FOS: Mathematics #Graph theory and applications #Markov Chains and Monte Carlo Methods #Probability (math.PR)

paper · pdf · doi:10.48550/arxiv.2307.01347

openalex publication_date 2023/07/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider an additive functional driven by a time-inhomogeneous Markov chain with a finite state space. Our study focuses on the joint distribution of the two-sided exit time and the state of the driving Markov chain at the time of exit, given in terms of expectation operators. These operators can be expressed as compositions of other operators related to some relevant one-sided exit (or first passage) problems. In addition, we study the law of the driving Markov chain at times prior to the exit time.

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