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

  • Walter A. Rosenkrantz (a1) and C. C. Y. Dorea (a2)


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'.


Corresponding author

Postal address: Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA 01003, U.S.A.


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

  • Walter A. Rosenkrantz (a1) and C. C. Y. Dorea (a2)


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