Elements of Stochastic Calculus via Regularisation

Francesco Russo (1) , Pierre Vallois (2, 3)

1 LAGA - Laboratoire Analyse, Géométrie et Applications
2 IECN - Institut Élie Cartan de Nancy
3 TOSCA - Simuler et calibrer des modèles stochastiques

This paper first summarizes the foundations of stochastic calculus via regularization and constructs through this procedure Itô and Stratonovich integrals. In the second part, a survey and new results are presented in relation with finite quadratic variation processes, Dirichlet and weak Dirichlet processes.

Mots clés: Integration via regularization; weak Dirichlet processes; covariation; Itô formulae.

Mots clés: Itô formulae

Domaines: Probabilités [math.PR]

Francesco Russo, Pierre Vallois. Elements of Stochastic Calculus via Regularisation. Séminaire de Probabilités, 2007, 1899-2007, pp.147-185. ⟨10.1007/978-3-540-71189-6_7⟩. ⟨hal-00020443⟩