Functional limit theorems for stochastic processes based on embedded processes

1 March 1975

journal article
research article
Published by Cambridge University Press (CUP) in Advances in Applied Probability

Vol. 7 (01) , 123-139
https://doi.org/10.1017/s0001867800040325

Abstract

The techniques used by Doeblin and Chung to obtain ordinary limit laws (central limit laws, weak and strong laws of large numbers, and laws of the iterated logarithm) for Markov chains, are extended to obtain analogous functional limit laws for stochastic processes which have embedded processes satisfying these laws. More generally, it is shown how functional limit laws of a stochastic process are related to those of a process embedded in it. The results herein unify and extend many existing limit laws for Markov, semi-Markov, queueing, regenerative, semi-stationary, and subordinated processes.

Keywords

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