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Basic results on Lévy processes. (English) Zbl 0974.60036
Barndorff-Nielsen, Ole E. (ed.) et al., Lévy processes. Theory and applications. Boston: Birkhäuser. 3-37 (2001).
Summary: The development of the theoretical study of Lévy processes is sketched with a formulation of some of the basic results. After (1) characterization and existence theorems, we focus on six main streams: (2) the study of stable processes, (3) extensions of the results on stable processes, (4) impetus from Hunt’s potential theory, (5) impetus from the theory of random walks, (6) distributional properties and self-decomposability, and (7) transformations of Lévy processes.
For the entire collection see [Zbl 0961.00012].

60G51 Processes with independent increments; Lévy processes
60G52 Stable stochastic processes
60G50 Sums of independent random variables; random walks