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Transactions of the American Mathematical Society

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

 

 

Stochastic waves


Authors: E. B. Dynkin and R. J. Vanderbei
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
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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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DOI: https://doi.org/10.1090/S0002-9947-1983-0682731-6
Article copyright: © Copyright 1983 American Mathematical Society