Some elements on Lévy processes (Q2734984)

This text is a brief survey about Lévy processes. It gives a dozen and a half of important theorems of the theory, most of which proofs can be found in the recent textbooks by the author [``Lévy processes'' (1996; Zbl 0861.60003)] and \textit{K. I. Sato} [``Lévy processes and infinitely divisible distributions'' (1999; Zbl 0973.60001)]. These theorems are concerned with the following topics (in order of appearance): integral functionals, renewal theory (with Dynkin-Lamperti theorem), fluctuation theory (with Wiener-Hopf factorization), recurrence and transience (with Spitzer-Rogozin's criterion, Erickson's and Chung-Fuchs' tests), sample path regularity (with Perkins' theorem on slow points for stable processes), and geometric properties of the range (with Evans-Fitzsimmons-Salisbury's theorem on multiple points).NEWLINENEWLINEFor the entire collection see [Zbl 0961.60001].