Eine Invarianzeigenschaft für Startverteilungen einer Klasse stochastischer Prozesse

Autor:	R. von Chossy, U. G. Oppel
Rok vydání:	1981
Předmět:	Statistics and Probability Discrete mathematics Pure mathematics Markov chain Mixing (mathematics) Stochastic process Ergodicity Discrete phase-type distribution Markov property Statistics Probability and Uncertainty Triviality Event (probability theory) Mathematics
Zdroj:	Metrika. 28:63-69
ISSN:	1435-926X 0026-1335
DOI:	10.1007/bf01902878
Popis:	This paper discusses some concepts of mixing for stochastic processes with discrete time. The idea of mixing, which is defined with respect to a starting distribution μ, means that the tranjectories of the process get out of any set with μ-measure zero with probability one. Such μ-mixing processes satisfy an invariance property; an asymptotic event has probability zero under any starting distribution, provided that it has probability zero under the starting distribution μ. Concerring stationary Markov chains these results imply a “weak” zero-one-law the relation of which with well-known “stronger” versions especially for aperiodic Harris chains and with the notions of weak ergodicity and a.s. triviality is studied.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::46ef98b1514c784269af79cf1c0d79ed https://doi.org/10.1007/bf01902878 Zobrazit plný text záznamu Full text from SpringerLink