Stochastic Differential Equations

Zeev Schuss*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

1 Scopus citations

Abstract

Dynamics driven by white noise, often written as (4.1) or is usually understood as the integral equation (4.2) where and are random coefficients, which can be interpreted in several different ways, depending on the interpretation of the stochastic integral in (4.2) as Itô, Stratonovich, backward, or otherwise. Different interpretations lead to very different solutions and to qualitative differences in the behavior of the solution. For example, a noisy dynamical system of the form (4.1) may be stable if the Itô integral is used in (4.2), but unstable if the Stratonovich or the backward integral is used instead. Different interpretations lead to different numerical schemes for the computer simulation of the equation. A different approach, based on path integrals, is given in Chapter 5.

Original languageEnglish
Title of host publicationApplied Mathematical Sciences (Switzerland)
PublisherSpringer
Pages92-132
Number of pages41
DOIs
StatePublished - 2010

Publication series

NameApplied Mathematical Sciences (Switzerland)
Volume170
ISSN (Print)0066-5452
ISSN (Electronic)2196-968X

Keywords

  • Brownian Motion
  • Conditional Expectation
  • Planck Equation
  • Stochastic Differential Equation
  • Uniqueness Theorem

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