Higher order PDE’s and iterated processes

Nane, Erkan

doi:10.1090/S0002-9947-07-04437-6

Higher order PDE’s and iterated processes
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by Erkan Nane PDF

Trans. Amer. Math. Soc. 360 (2008), 2681-2692 Request permission

Abstract:

We introduce a class of stochastic processes based on symmetric $\alpha$-stable processes, for $\alpha \in (0,2]$. These are obtained by taking Markov processes and replacing the time parameter with the modulus of a symmetric $\alpha$-stable process. We call them $\alpha$-time processes. They generalize Brownian time processes studied in Allouba and Zheng (2001), Allouba (2002), (2003), and they introduce new interesting examples. We establish the connection of $\alpha$-time processes to some higher order PDE’s for $\alpha$ rational. We also obtain the PDE connection of subordinate killed Brownian motion in bounded domains of regular boundary.

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