Discrete sampling of functionals of Itô processes

Emmanuel Gobet (1) , Stéphane Menozzi (2)

1 MATHFI - Mathématiques financières
2 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

For a multidimensional Ito process $(X_t)_{t \ge 0} $ driven by a Brownian motion, we are interested in approximating the law of $\psi\left((X_s)_{s\in [0,T]}\right)$, $T>0$ deterministic, for a given functional $\psi$ using a discrete sample of the process $X$. For various functionals (related to the maximum, to the integral of the process, or to the killed/stopped path) we extend to the non Markovian framework of Itô processes the results available in the diffusion case. We thus prove that the order of convergence is more specifically linked to the Brownian driver and not to the Markov property of SDEs.

Domaines: Probabilités [math.PR]

Emmanuel Gobet, Stéphane Menozzi. Discrete sampling of functionals of Itô processes. Catherine Donati-Martin, Michel Emery, Alain Rouault, Christophe Stricker. Séminaire de probabilités XL, Springer, pp.355-374, 2007, Lecture Notes in Mathematics n°1899, ⟨10.1007/978-3-540-71189-6_19⟩. ⟨hal-00168857⟩