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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Ergodic behaviour of nonstationary regenerative processes
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by David McDonald PDF
Trans. Amer. Math. Soc. 255 (1979), 135-152 Request permission

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 $\lim \limits _{n \to \infty } (1/n)\Sigma _{j = 1}^n {\mu _j} = \mu$ and $\lim \limits _{n \to \infty } (1/n)\Sigma _{j = 1}^n {\alpha _j} = \alpha$.
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Additional Information
  • © Copyright 1979 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 255 (1979), 135-152
  • MSC: Primary 60K05
  • DOI: https://doi.org/10.1090/S0002-9947-1979-0542874-3
  • MathSciNet review: 542874