A class of CTRWs: Compound fractional poisson processes
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This chapter is an attempt to present a mathematical theory of compound fractional Poisson processes. It begins with the characterization of a well-known Lévy process: The compound Poisson process. The semi-Markov extension of the compound Poisson process naturally leads to the compound fractional Poisson process, where the Poisson counting process is replaced by the Mittag- Leffler counting process also known as fractional Poisson process. This process is no longer Markovian and Lévy. However, several analytical results are available and some of them are discussed here. © 2012 by World Scientific Publishing Co. Pte. Ltd. All rights reserved.