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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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Stochastic waves
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by E. B. Dynkin and R. J. Vanderbei PDF
Trans. Amer. Math. Soc. 275 (1983), 771-779 Request permission

Abstract:

Let $\phi$ be a real valued function defined on the state space of a Markov process ${x_t}$. Let ${\tau _t}$ be the first time ${x_t}$ gets to a level set of $\phi$ which is $t$ units higher than the one on which it started. We call the time changed process $\tilde {x}_{t} = x_{{\tau _t}}$ a stochastic wave. We give conditions under which this process is Markovian and we evaluate its infinitesimal operator.
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Additional Information
  • © Copyright 1983 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 275 (1983), 771-779
  • MSC: Primary 60J25
  • DOI: https://doi.org/10.1090/S0002-9947-1983-0682731-6
  • MathSciNet review: 682731