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 in the Watanabe spaces and with respect to the spatial variable in the deterministic Sobolev spaces.
2D-Stochastic Currents over the Wiener Sheet
Flandoli, Franco;
2014
Abstract
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 in the Watanabe spaces and with respect to the spatial variable in the deterministic Sobolev spaces.File in questo prodotto:
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