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Doeblin’s big limit theorem. (English) Zbl 0786.60099

Summary: W. Doeblin regarded his paper [Ann. École Norm., III. Sér. 57, 61-111 (1940; Zbl 0024.26503)] as his hardest work. The big limit is that of \(P^{(n)}(x,E)\) as \(n\) tends to infinity, in a measurable non- topologized space. An exposition of part one of this paper was published by the author [Z. Wahrscheinlichkeitstheorie Verw. Geb. 2, 230-254 (1964; Zbl 0119.346)]. This is the exposition of part two, which contains some reparation as well as clarification.

MSC:

60J25 Continuous-time Markov processes on general state spaces
60F05 Central limit and other weak theorems
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References:

[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.? · Zbl 0119.34604
[2] Doeblin, W. (1940). ?lements d’une th?orie g?n?rale des cha?nes simples constantes de Markoff.Ann. Sci. ?cole Norm. Sup. (3),57 (2), 61-11. · Zbl 0024.26503
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