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

Sylvain Maire (1) , Etienne Tanré (1)

1 TOSCA - Simuler et calibrer des modèles stochastiques

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.

Domaines: Probabilités [math.PR]

Sylvain Maire, Etienne Tanré. Some new simulations schemes for the evaluation of Feynman-Kac representations. Monte Carlo Methods and Applications, 2008, 14 (1), pp.29--51. ⟨10.1515/MCMA.2008.002⟩. ⟨inria-00182436⟩