Levy Processes and Stochastic Calculus

2. Auflage 2014
ISBN: 978-0-521-73865-1
Verlag: Cambridge University Press

Buch, Englisch, Band 116, 490 Seiten, Format (B × H): 152 mm x 229 mm, Gewicht: 792 g

Reihe: Cambridge Studies in Advanced Mathematics

Lévy 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 Lévy processes, then leading on to develop the stochastic calculus for Lévy 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 Lévy processes to have finite moments; characterisation of Lévy processes with finite variation; Kunita's estimates for moments of Lévy type stochastic integrals; new proofs of Ito representation and martingale representation theorems for general Lévy processes; multiple Wiener-Lévy integrals and chaos decomposition; an introduction to Malliavin calculus; an introduction to stability theory for Lévy-driven SDEs.

Autoren/Hrsg.

Applebaum, David

Fachgebiete

• Mathematik | Informatik Mathematik Stochastik Elementare Stochastik
• Mathematik | Informatik Mathematik Mathematische Analysis
• Mathematik | Informatik Mathematik Stochastik Stochastische Prozesse

Inhaltsverzeichnis

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.

Über Autor(innen)

Applebaum, David
David Applebaum is a Professor in the Department of Probability and Statistics at the University of Sheffield.