Asymptotics of Markov Additive Chains on a Half-Plane: A Ratio Limit Theorem

Autor:	Aziz Khanchi
Rok vydání:	2011
Předmět:	Statistics and Probability Markov kernel Markov chain mixing time Markov chain General Mathematics Mathematical analysis Markov process symbols.namesake symbols Balance equation Additive Markov chain Markov property Limit (mathematics) Statistics Probability and Uncertainty Mathematics
Zdroj:	Journal of Theoretical Probability. 25:62-76
ISSN:	1572-9230 0894-9840
DOI:	10.1007/s10959-011-0384-1
Popis:	Consider a Markov additive chain (V,Z) with a negative horizontal drift on a half-plane. We provide the limiting distribution of Z when V passes a threshold for the first time, as V tends to infinity. Our contribution is to allow the Markovian part of an associated twisted Markov chain to be null recurrent or transient. The positive recurrent case was treated by Kesten [Ann. Probab. 2 (1974), 355–386]. Moreover, a ratio limit will be established for a transition kernel with unbounded jumps.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::9a934b0a1082559b1ed29ff92bec7961 https://doi.org/10.1007/s10959-011-0384-1 Zobrazit plný text záznamu Full text from SpringerLink