STABILITY OF OVERSHOOTS OF MARKOV ADDITIVE PROCESSES

• 成果类型: Article
• 署名作者: Doeringa, Leif; Trottnerb, Lukas
• 署名单位: University of Mannheim
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/23-AAP1951
• 发表日期: 2023
• 页码: 5413-5458
• 关键词: renewal theory; ruin probabilities; fluctuation theory; LIMIT-THEOREMS; Levy processes; CONVERGENCE; ergodicity; functionals; discrete; lyapunov

摘要

We prove precise stability results for overshoots of Markov additive processes (MAPs) with finite modulating space. Our approach is based on the Markovian nature of overshoots of MAPs whose mixing and ergodic proper-ties are investigated in terms of the characteristics of the MAP. On our way we extend fluctuation theory of MAPs, contributing among others to the understanding of the Wiener-Hopf factorization for MAPs by generalizing Vigon's equations amicales inverses known for Levy processes. Using the Lamperti transformation the results can be applied to self-similar Markov processes. Among many possible applications, we study the mixing behavior of stable processes sampled at symmetric first hitting times as a concrete example.