Stochastic Differential Equations Driven by Processes Generated by Divergence Form Operators I: A Wong-Zakai Theorem

Antoine Lejay (1, 2)

1 IECN - Institut Élie Cartan de Nancy
2 OMEGA - Probabilistic numerical methods

We show in this article how the theory of "rough paths" allows us to construct solutions of differential equations (SDEs) driven by processes generated by divergence-form operators. For that, we use approximations of the trajectories of the stochastic process by piecewise smooth paths. A result of type Wong-Zakai follows immediately.

Mots clés: Rough paths; stochastic differential equations; stochastic process generated by divergence-form operators; Dirichlet process; approximation of trajectories

Domaines: Probabilités [math.PR]

Antoine Lejay. Stochastic Differential Equations Driven by Processes Generated by Divergence Form Operators I: A Wong-Zakai Theorem. ESAIM: Probability and Statistics, 2006, 10, pp.356-379. ⟨10.1051/ps:2006015⟩. ⟨inria-00092426⟩