David Applebaum

Levy Processes and Stochastic Calculus (eBook, PDF)

• Format: PDF

Produktbeschreibung

Levy processes form a wide and rich class of random process, and have many applications ranging from physics to finance. Stochastic calculus is the mathematics of systems interacting with random noise. Here, the author ties these two subjects together, beginning with an introduction to the general theory of Levy processes, then leading on to develop the stochastic calculus for Levy processes in a direct and accessible way. This fully revised edition now features a number of new topics. These include: regular variation and subexponential distributions; necessary and sufficient conditions for Levy processes to have finite moments; characterisation of Levy processes with finite variation; Kunita's estimates for moments of Levy type stochastic integrals; new proofs of Ito representation and martingale representation theorems for general Levy processes; multiple Wiener-Levy integrals and chaos decomposition; an introduction to Malliavin calculus; an introduction to stability theory for Levy-driven SDEs.

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Produktdetails

• Verlag: Cambridge University Press
• Erscheinungstermin: 30. April 2009
• Englisch
• ISBN-13: 9780511530784
• Artikelnr.: 38210624

Autorenporträt

David Appelbaum has previously worked at a University as well as in publishing. His most recent books include notes on water: an aqueous phenomenology [Monkfish, 2018].

Inhaltsangabe

Preface to second edition
Preface to first edition
Overview
Notation
1. Lévy processes
2. Martingales, stopping times and random measures
3. Markov processes, semigroups and generators
4. Stochastic integration
5. Exponential martingales
6. Stochastic differential equations
References
Index of notation
Subject index.