Higher order PDE's and iterated processes

We introduce a class of stochastic processes based on symmetric alpha-stable processes, for alpha epsilon (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.