Some elements on Lévy processes

Abstract

This chapter provides a brief survey of some of the most salient features of the theory. It presents the fundamental aspects of Levy processes (Markov property and infinite divisibility) and describes their probabilistic structure. The chapter focuses on various techniques used to derive the distribution of certain important functional of Levy processes. The chapter concludes with some remarkable sample path properties such as transience or recurrence, information on the rate of growth, and certain geometric properties of the range.