Pseudo Differential Operators and Markov Processes, Volume III: Markov Processes and Applications

This volume concentrates on how to construct a Markov process by starting with a suitable pseudo-differential operator. Feller processes, Hunt processes associated with Lp-sub-Markovian semigroups and processes constructed by using the Martingale problem are at the center of the considerations. The potential theory of these processes is further developed and applications are discussed. Due to the non-locality of the generators, the processes are jump processes and their relations to Levy processes are investigated. Special emphasis is given to the symbol of a process, a notion which generalizes that of the characteristic exponent of a Levy process and provides a natural link to pseudo-differential operator theory.