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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Some limit theorems for nonhomogeneous Markoff processes

Author: A. Fuchs
Journal: Trans. Amer. Math. Soc. 86 (1957), 511-531
MSC: Primary 60.00
MathSciNet review: 0094848
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Abstract: We intend to study some problems related to the asymptotic behaviour of a physical system the evolution of which is markovian. The typical example of such an evolution is furnished by an homogeneous discrete chain with a finite number of possible states considered first by A. A. Markoff. In §1 we recall briefly the main results of this theory and in §2 we treat its obvious generalization to the continuous parameter case. In §3 we pass to the proper object of this paper and we establish a limit theorem for time-homogeneous Markoff processes. This limit theorem is then extended to the nonhomogeneous case under some supplementary conditions (§4). Finally we give an application of this theory to random functions connected with a Markoff process (§5).

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Article copyright: © Copyright 1957 American Mathematical Society