Stochastic Differential Equations Driven by Processes Generated by Divergence Form Operators II: Convergence results

Antoine Lejay (1, 2)

1 IECN - Institut Élie Cartan de Nancy
2 TOSCA - Simuler et calibrer des modèles stochastiques

We have seen in a previous article how the theory of "rough paths" allows us to construct solutions of differential equations driven by processes generated by divergence form operators. In this article, we study a convergence criterion which implies that one can interchange the integral with the limit of a family of stochastic processes generated by divergence form operators. As a corollary, we identify stochastic integrals constructed with the theory of rough paths with Stratonovich or Itô integrals already constructed for stochastic processes generated by divergence form operators by using time-reversal techniques.

Mots clés: Rough paths; stochastic differential equations; stochastic process generated by divergence form operators; Condition UTD; convergence of stochastic integrals

Domaines: Probabilités [math.PR]

Antoine Lejay. Stochastic Differential Equations Driven by Processes Generated by Divergence Form Operators II: Convergence results. ESAIM: Probability and Statistics, 2008, 12, pp.387-411. ⟨10.1051/ps:2007040⟩. ⟨inria-00092427v3⟩