Premium
Infinitely Divisible Distributions as Limit Laws for Sums of Random Variables Connected in a Markov Chain
Author(s) -
Heinrich Lothar
Publication year - 1982
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19821070109
Subject(s) - markov chain , mathematics , mathematical economics , limit (mathematics) , random variable , citation , combinatorics , philosophy , calculus (dental) , law , statistics , political science , mathematical analysis , medicine , dentistry
Here ((E,.&)k=,,, ,.,., kn)*=,,2 ,.,. is a sequence of MABKOV processes, (.(ZPk, gd) denotes the state space of &&k, g, is a real-valued gnk-ineasurable function on Qnk, p r ) ( o , A ) denotes the transition fundion (from astate WEIR,,-, intoaset AEBd) and py’(A) stands for the initial distribution of (Ea), =f,2,...,kit. 1) To describe the weak dependence between RVCMC (in the same row) it is usually used the ergodicity coefficient in the first k, steps of the MARKOV process (in the nt,h row) defined by a@)= min (I sup lpr)(co, A ) -g$) (6, A ) / ) , (see [i2]). 2 S k S k n uJ,aJ€I?&-l AcBnk Throughout this paper we assume