Doeblin's big limit theorem
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Doeblin regarded his paper(2) as his hardest work. The big limit is that ofP(n)(x, E) asn tends to infinity, in a measurable non-topologized space. An exposition of part one of this paper was published in Ref. 1. This is the exposition of part two, which contains some reparation as well as clarification.
Key WordsMarkov processes limit theory
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- 1.Chung, K. L. (1964). The general theory of Markov processes according to Doeblin. Z. Wahrscheinlichkeitstheorie2, 230–254. See also Errata, loc. cit.12, 172 (1969). On p. 239, line 9, insert “or empty” at end; on p. 241, line 7, read “indecomp.” for “decomp.”Google Scholar
- 2.Doeblin, W. (1940). Élements d'une théorie générale des chaînes simples constantes de Markoff.Ann. Sci. École Norm. Sup. (3),57 (2), 61–11.Google Scholar