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Asymptotic expansions in the central limit theorem for compound and Markov processes

Research paper by Christian Hipp

Indexed on: 01 Sep '85Published on: 01 Sep '85Published in: Probability Theory and Related Fields



Abstract

For independent identically distributed bivariate random vectors (X1, Y1), (X2, Y2), ... and for large t the distribution of X1 +...+ XN(t) is approximated by asymptotic expansions. Here N(t) is the counting process with lifetimes Y1, Y2,.... Similar expansions are derived for multivariate X1. Furthermore, local asymptotic expansions are valid for the distribution of f(X1)+ ...+ f(XN) when N is large and nonrandom, and Xi, i=1, 2,..., is a discrete strongly mixing Markov chain.