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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)


Ergodic behaviour of nonstationary regenerative processes

Author: David McDonald
Journal: Trans. Amer. Math. Soc. 255 (1979), 135-152
MSC: Primary 60K05
MathSciNet review: 542874
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Abstract: Let $ {V_t}$ be a regenerative process whose successive generations are not necessarily identically distributed and let A be a measurable set in the range of $ {V_t}$. Let $ {\mu _n}$ be the mean length of the nth generation and $ {\alpha _n}$ be the mean time $ {V_t}$ is in A during the nth generation. We give conditions ensuring $ {\lim _{t \to \infty }}\,\operatorname{prob} \{ \,{V_t}\, \in \,A\,\} \, = \,\alpha /\mu $ where $ \mathop {\lim }\limits_{n \to \infty } (1/n)\Sigma _{j = 1}^n\,{\mu _j}\, = \mu $ and $ \mathop {\lim }\limits_{n \to \infty } (1/n)\Sigma _{j = 1}^n\,{\alpha _j}\, = \,\alpha $.

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Additional Information

PII: S 0002-9947(1979)0542874-3
Keywords: Nonstationary regenerative limits
Article copyright: © Copyright 1979 American Mathematical Society