Stochastic waves

Dynkin, E. B.; Vanderbei, R. J.

doi:10.1090/S0002-9947-1983-0682731-6

Stochastic waves
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by E. B. Dynkin and R. J. Vanderbei

Trans. Amer. Math. Soc. 275 (1983), 771-779

DOI: https://doi.org/10.1090/S0002-9947-1983-0682731-6

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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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