2D- stochastic currents over the Wiener sheet

Franco Flandoli (1) , Peter Imkeller (2) , Ciprian Tudor (3)

1 DMA - Dipartimento di Matematica Applicata [Pisa]
2 Institut für Mathematik [Berlin]
3 LPP - Laboratoire Paul Painlevé - UMR 8524

By using stochastic calculus for two-parameter processes and chaos expansion into multiple Wiener-Itô integrals, we define a 2D-stochastic current over the Brownian sheet. This concept comes from geometric measure theory. We also study the regularity of the stochastic current with respect to the randomness variable in the Watanabe spaces and with respect to the spatial variable in the deterministic Sobolev spaces.

Domaines: Probabilités [math.PR]

Franco Flandoli, Peter Imkeller, Ciprian Tudor. 2D- stochastic currents over the Wiener sheet. 2012. ⟨hal-00665865v2⟩