Higher order PDE’s and iterated processes
- 20 December 2007
- journal article
- Published by American Mathematical Society (AMS) in Transactions of the American Mathematical Society
- Vol. 360 (5) , 2681-2692
- https://doi.org/10.1090/s0002-9947-07-04437-6
Abstract
We introduce a class of stochastic processes based on symmetric α \alpha -stable processes, for α ∈ ( 0 , 2 ] \alpha \in (0,2] . These are obtained by taking Markov processes and replacing the time parameter with the modulus of a symmetric α \alpha -stable process. We call them α \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 α \alpha -time processes to some higher order PDE’s for α \alpha rational. We also obtain the PDE connection of subordinate killed Brownian motion in bounded domains of regular boundary.Keywords
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