Reminiscences of one of Doeblin’s papers. (English) Zbl 0788.60081

Cohn, Harry (ed.), Doeblin and modern probability. Proceedings of the Doeblin conference ‘50 years after Doeblin: development in the theory of Markov chains, Markov processes, and sums of random variables’ held November 2-7, 1991 at the University of Tübingen’s Heinrich Fabri Institut, Blaubeuren, Germany. Providence, RI: American Mathematical Society. Contemp. Math. 149, 65-71 (1993).
W. Doeblin’s paper commented by the author is “Sur deux problèmes de M. Kolmogoroff concernant les chaînes dénombrables” [Bull. Soc. Math. Fr. 66, 210-220 (1938; Zbl 0020.14604)]. The author stresses the importance of Doeblin’s ideas concerning ratio limit theorems for sums of transition probabilities and the reduction of the problem of the asymptotic behaviour of partial sums associated with a recurrent Markov chain to one for sums of independent and identically distributed random variables.
For the entire collection see [Zbl 0777.00028].


60J10 Markov chains (discrete-time Markov processes on discrete state spaces)
60-03 History of probability theory
60-02 Research exposition (monographs, survey articles) pertaining to probability theory
60F05 Central limit and other weak theorems

Biographic References:

Doeblin, W.


Zbl 0020.14604