Mimicking the marginal distributions of a semimartingale

Amel Bentata (1) , Rama Cont (1)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

We show that the flow of marginal distributions of a discontinuous semimartingale X can be matched by a Markov process whose infinitesimal generator is expressed in terms of the local characteristics of X. Our results extend a ``mimicking theorem" of Gyongy (1986) to discontinuous semimartingales. We use this result to derive a partial integro-differential equation for the one-dimensional distributions of a semimartingale, extending the Kolmogorov forward equation to a non-Markovian setting.

Mots clés: mimicking theorems; semimartingale; martingale problem; integro-differential operator

Domaines: Probabilités [math.PR]

Amel Bentata, Rama Cont. Mimicking the marginal distributions of a semimartingale. 2009. ⟨hal-00425345v2⟩