Lévy processes and stochastic calculus

書誌事項

Lévy processes and stochastic calculus

David Applebaum

(Cambridge studies in advanced mathematics, 116)

Cambridge University Press, c2009

2nd ed

  • : pbk

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注記

Reprinted 2011 with corrections, 2013 with corrections

Includes bibliographical references (p. 431-448) and indexes

内容説明・目次

内容説明

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.

目次

  • Preface to second edition
  • Preface to first edition
  • Overview
  • Notation
  • 1. Levy 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.

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