A scheme for simulating one-dimensional diffusion processes with discontinuous coefficients

Antoine Lejay (1, 2) , Miguel Martinez (1)

1 OMEGA - Probabilistic numerical methods
2 IECN - Institut Élie Cartan de Nancy

The aim of this article is to provide a scheme for simulating diffusion processes evolving in one-dimensional discontinuous media. This scheme does not rely on smoothing the coefficients that appear in the infinitesimal generator of the diffusion processes, but uses instead an exact description of the behavior of their trajectories when they reach the points of discontinuity. This description is supplied with the local comparison of the trajectories of the diffusion processes with those of a Skew Brownian Motion.

Mots clés: Monte Carlo methods; Skew Brownian motion; Divergence form operator; One-dimensional diffusion; Local time; Scale function; Speed measure

Domaines: Analyse numérique [math.NA]; Probabilités [math.PR]

Antoine Lejay, Miguel Martinez. A scheme for simulating one-dimensional diffusion processes with discontinuous coefficients. The Annals of Applied Probability, 2006, 16 (1), pp.107-139. ⟨10.1214/105051605000000656⟩. ⟨inria-00000410⟩