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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 variable in the Watanabe spaces and with respect to the spatial variable in the deterministic Sobolev spaces.'
author:
- |
    Franco Flandoli$^{1}, $Peter Imkeller $^{2}\qquad $Ciprian A. Tudor $^{3, 4}$ [^1]\
    $^{1}$Dipartimento di Matematica Applicata, Universita di Pisa,\
    Via Bonnano 25B, I-56126, Pisa, Italy\
    flandoli@dma.unipi.it\
    $^{2}$Institut für Mathematik, Humboldt-Universität zu Berlin\
    , Unter den Linden 6, 10099 Berlin, Germany,\
    imkeller@mathematik.hu-berlin.de\
    $^{3}$ Laboratoire Paul Painlevé, Université de Lille 1\
    F-59655 Villeneuve d’Ascq, France,\
    $^{4}$ Department of Mathematics,\
    Academy of Economical Studies, Bucharest, Romania\
    tudor@math.univ-lille1.fr
date:  
title: '2D- stochastic currents over the Wiener sheet [^2]'
---

0.5cm

[**2000 AMS Classification Numbers:**]{} 60G15, 60G18, 60H05, 76M35, 60H05

0.3cm

[**Key words:**]{} currents, multiple stochastic integrals, Brownian sheet, two-parameter processes

Introduction
============

The purpose of this paper is to study two-dimensional stochastic currents. The concept of current comes from geometric measure theory. Let us briefly recall a few definitions on deterministic currents used in the sequel. More informations can 