Approximation of multiple stochastic integrals and its application to stochastic differential equations

C. W. Li, X. Q. Liu

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review

15 Citations (Scopus)

Abstract

As multiple stochastic integrals are not very easy to simulate, we would like to treat them as solutions of systems of stochastic differential equations and solve them successively and recursively approximated by the stochastic Taylor expansion as a Chen series in terms of a Philip Hall basis or Lyndon basis. We can save sufficient values of multiple stochastic integrals with independent sample paths in a look-up table for future use. The table can be used to implement high order schemes to solve stochastic differential equations numerically. A numerical example will be shown to illustrate the efficiency.
Original languageEnglish
Pages (from-to)697-708
JournalNonlinear Analysis, Theory, Methods and Applications
Volume30
Issue number2
DOIs
Publication statusPublished - Dec 1997

Research Keywords

  • Brownian motions
  • Chen series
  • Lyndon basis
  • Multiple Ito integrals
  • Philip hall basis
  • Shuffle algebra
  • Strong discretization

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