WIAS Preprint No. 855, (2003)

Approximation of Wiener integrals with respect to the Brownian bridge by simulation of SDEs



Authors

  • Milstein, Grigori N.
  • Tretyakov, Michael V.

2010 Mathematics Subject Classification

  • 65C30 28C20 65C05 60H35

Keywords

  • Conditional Wiener integrals, Feynman path integrals, numerical integration of stochastic differential equations, Monte Carlo simulation

DOI

10.20347/WIAS.PREPRINT.855

Abstract

Numerical integration of stochastic differential equations together with the Monte Carlo technique is used to evaluate conditional Wiener integrals of exponential-type functionals. An explicit Runge-Kutta method of order four and implicit Runge-Kutta methods of order two are constructed. The corresponding convergence theorems are proved. To reduce the Monte Carlo error, a variance reduction technique is considered. Results of numerical experiments are presented.

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