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Some new simulations schemes for the evaluation of Feynman–Kac representations

Author

Listed:
  • Maire Sylvain

    (ISITV, Université de Toulon et du Var, avenue G. Pompidou, BP 56, 83262 La Valette du Var CEDEX, France. Email: maire@univ-tln.fr)

  • Tanré Etienne

    (INRIA, Equipe Projet TOSCA, 2004 route des Lucioles, BP93, 06902 Sophia-Antipolis, France. Email: Etienne.Tanre@sophia.inria.fr)

Abstract

We describe new variants of the Euler scheme and of the walk on spheres method for the Monte Carlo computation of Feynman–Kac representations. We optimize these variants using quantization for both source and boundary terms. Numerical tests are given on basic examples and on Monte Carlo versions of spectral methods for the Poisson equation. We especially introduce a new stochastic spectral formulation with very good properties in terms of conditioning.

Suggested Citation

  • Maire Sylvain & Tanré Etienne, 2008. "Some new simulations schemes for the evaluation of Feynman–Kac representations," Monte Carlo Methods and Applications, De Gruyter, vol. 14(1), pages 29-51, January.
    • Handle: RePEc:bpj:mcmeap:v:14:y:2008:i:1:p:29-51:n:2
    DOI: 10.1515/MCMA.2008.002
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    References listed on IDEAS

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    1. Gobet, Emmanuel, 2000. "Weak approximation of killed diffusion using Euler schemes," Stochastic Processes and their Applications, Elsevier, vol. 87(2), pages 167-197, June.
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