Adaptive weak approximation of diffusions with jumps

E. Mordecki*, A. Szepessy, Raul Tempone, G. E. Zouraris

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

21 Scopus citations

Abstract

This work develops adaptive time stepping algorithms for the approximation of a functional of a diffusion with jumps based on a jump augmented Monte Carlo Euler-Maruyama method, which achieve a prescribed precision. The main result is the derivation of new expansions for the time discretization error, with computable leading order term in a posteriori form, which are based on stochastic flows and discrete dual backward functions. Combined with proper estimation of the statistical error, they lead to efficient and accurate computation of global error estimates, extending the results by A. Szepessy, R. Tempone, and G. E. Zouraris [Comm. Pure Appl. Math., 54 (2001), pp. 1169-1214]. Adaptive algorithms for either deterministic or trajectory-dependent time stepping are proposed. Numerical examples show the performance of the proposed error approximations and the adaptive schemes.

Original languageEnglish (US)
Pages (from-to)1732-1768
Number of pages37
JournalSIAM Journal on Numerical Analysis
Volume46
Issue number4
DOIs
StatePublished - Nov 10 2008

Keywords

  • A posteriori error estimates
  • Backward dual functions
  • Diffusions with jumps
  • Error control
  • Euler-Maruyama method
  • Weak approximation

ASJC Scopus subject areas

  • Numerical Analysis
  • Computational Mathematics
  • Applied Mathematics

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