On the decomposition of excursions measures of processes whose generators have diffusion coefficients discontinuous at one point

Antoine Lejay (1, 2)

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

The coefficients in the decomposition of the excursions measure as convex combination of excursions measures of reflected processes are computed in order to characterize the discontinuity at one point of the diffusion coefficient. In some sense, this result extends to general diffusions a similar one for the skew Brownian motion, and we advocate it may be used in Monte Carlo methods for discontinuous media.

Mots clés: scale function and speed measure; excursions theory; skew Brownian motion; Monte Carlo methods

Domaines: Probabilités [math.PR]

Antoine Lejay. On the decomposition of excursions measures of processes whose generators have diffusion coefficients discontinuous at one point. Markov Processes And Related Fields, 2002, 8 (1), pp.117-126. ⟨inria-00001230⟩