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

1980; Cambridge University Press; Volume: 17; Issue: 3 Linguagem: Inglês

10.2307/3212964

1475-6072

Walter A. Rosenkrantz, Chang C. Y. Dorea,

advanced mathematical theories

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'.