ON STABLE MARKOV-PROCESSES

Necessary conditions are given for a symmetric α-stable (SαS) process, 1 < α < 2, to be Markov. These conditions are then applied to find Markov or weakly Markov processes within certain important classes of SαS processes: time changed Lévy motion, scale mixed Gaussian processes, moving averages and harmonizable processes. Two stationary SαS Markov processes are introduced, the right and the left SαS Ornstein-Uhlenbeck processes. Some of the results are in sharp contrast to the Gaussian case α = 2. © 1990.