2D- stochastic currents over the Wiener sheet

Details 2D- stochastic currents over the Wiener sheet 2D- stochastic currents over the Wiener sheet

2012-02-03

arxiv.org/abs/1202.0618v1

Mathematics

Probability

Scientific paper

By using stochastic calculus for two-parameter processes and chaos expansion into multiple Wiener-It\^o 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.

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