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Limit theorems for Markov processes via a variant of the Trotter-Kato theorem

Published online by Cambridge University Press:  14 July 2016

Walter A. Rosenkrantz  and
C. C. Y. Dorea
Walter A. Rosenkrantz*
Affiliation:
University of Massachusetts
C. C. Y. Dorea
Affiliation:
Universidade de Brasilia
*
∗Postal address: Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA 01003, U.S.A.
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Abstract

A variant of the Trotter–Kato theorem due to Kurtz (1969) is used to give new and simpler proofs of functional central limit theorems for Markov processes. Applications include theorems of Bellman and Harris (1951), Stone (1961), Karlin and McGregor (1965), Gihman and Skorokhod (1972) and Rosenkrantz (1975). In addition our methods yield a novel counterexample to the so-called ‘diffusion approximation'.

Keywords

MARKOV PROCESSESFUNCTIONAL CENTRAL LIMIT THEOREMSTROTTER-KATO THEOREM
Type
Research Papers
Information
Journal of Applied Probability , Volume 17 , Issue 3 , September 1980 , pp. 704 - 715
Copyright
Copyright © Applied Probability Trust 1980 

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Footnotes

Research supported by U.S. Air Force Office of Scientific Research under Contract F4962079-C-0209.

∗∗

Universidade de Brasilia, Departamento de Mathematica, 1E 70.000 Brasilia DF, Brazil.

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