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Continuous-Path Random Processes: Mathematical Prerequisites

  • Monique JeanblancEmail author
  • Marc Yor
  • Marc Chesney
Chapter
  • 3.9k Downloads
Part of the Springer Finance book series (FINANCE)

Abstract

Historically, in mathematical finance, continuous-time processes have been considered from the very beginning, e.g., Bachelier [39, 41] deals with Brownian motion, which has continuous paths. This may justify making our starting point in this book to deal with continuous-path random processes, for which, in this first chapter, we recall some well-known facts. We try to give all the definitions and to quote all the important facts for further use. In particular, we state, without proofs, results on stochastic calculus, change of probability and stochastic differential equations.

Keywords

Brownian Motion Local Martingale Mathematical Prerequisite Integrable Martingale Bounded Borel Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag London 2009

Authors and Affiliations

  1. 1.Dépt. MathématiquesUniversité d’EvryEvryFrance
  2. 2.Labo. Probabilités et Modèles AléatoiresUniversité Paris VIParisFrance
  3. 3.Inst. Schweizerisches Bankwesen (ISB)Universität ZürichZürichSwitzerland

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