Itô's formula for linear fractional PDEs

Jorge A. Leon (1) , Samy Tindel (2, 3)

1 CINVESTAV-IPN - Departamento de Control Automático
2 IECN - Institut Élie Cartan de Nancy
3 TOSCA - Simuler et calibrer des modèles stochastiques

In this paper we introduce a stochastic integral with respect to the solution X of the fractional heat equation on [0,1], interpreted as a divergence operator. This allows to use the techniques of the Malliavin calculus in order to establish an Itô-type formula for the process X.

Mots clés: Heat equation; fractional Brownian motion; Itô's formula

Domaines: Probabilités [math.PR]

Jorge A. Leon, Samy Tindel. Itô's formula for linear fractional PDEs. Stochastics: An International Journal of Probability and Stochastic Processes, 2008, 80, pp.427-450. ⟨10.1080/17442500701661687⟩. ⟨hal-00109832⟩