Lévy matters. III : Lévy-type processes : construction, approximation and sample path properties / Björn Böttcher, René Schilling, Jian Wang

Auteur: Böttcher, Björn - AuteurCo-auteur: Schilling, René (1969-) - Auteur ; Wang, Jian - AuteurType de document: Livre numériqueCollection: Lecture notes in mathematics ; 2099Langue: anglaisÉditeur: New York : Springer, cop. 2013 ISBN: 9783319026831 Note: Publisher’s description: This volume presents recent developments in the area of Lévy-type processes and more general stochastic processes that behave locally like a Lévy process. Although written in a survey style, quite a few results are extensions of known theorems, and others are completely new. The focus is on the symbol of a Lévy-type process: a non-random function which is the counterpart of the characteristic exponent of a Lévy process. The class of stochastic processes which can be associated with a symbol is characterized, various schemes constructing a stochastic process from a given symbol are discussed, and it is shown how one can use the symbol in order to describe the sample path properties of the underlying process. Lastly, the symbol is used to approximate and simulate Lévy-type processes. This is the third volume in a subseries of the Lecture Notes in Mathematics called Lévy Matters. Each volume describes a number of important topics in the theory or applications of Lévy processes and pays tribute to the state of the art of this rapidly evolving subject with special emphasis on the non-Brownian world. Sujets MSC: 60G51 Probability theory and stochastic processes -- Stochastic processes -- Processes with independent increments; Lévy processes
60J25 Probability theory and stochastic processes -- Markov processes -- Continuous-time Markov processes on general state spaces
60J75 Probability theory and stochastic processes -- Markov processes -- Jump processes
01A70 History and biography -- History of mathematics and mathematicians -- Biographies, obituaries, personalia, bibliographies
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Publisher’s description: This volume presents recent developments in the area of Lévy-type processes and more general stochastic processes that behave locally like a Lévy process. Although written in a survey style, quite a few results are extensions of known theorems, and others are completely new. The focus is on the symbol of a Lévy-type process: a non-random function which is the counterpart of the characteristic exponent of a Lévy process. The class of stochastic processes which can be associated with a symbol is characterized, various schemes constructing a stochastic process from a given symbol are discussed, and it is shown how one can use the symbol in order to describe the sample path properties of the underlying process. Lastly, the symbol is used to approximate and simulate Lévy-type processes.

This is the third volume in a subseries of the Lecture Notes in Mathematics called Lévy Matters. Each volume describes a number of important topics in the theory or applications of Lévy processes and pays tribute to the state of the art of this rapidly evolving subject with special emphasis on the non-Brownian world.

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