A White Noise Approach to Stochastic Currents of Brownian Motion

Abstract

In this paper we study stochastic currents of Brownian motion $\xi (x)$, $x\in {\mathbb{R}}^d$, by using white noise analysis. For $x\in {\mathbb{R}}^d\backslash \{0\}$ and for $x=0\in \mathbb{R}$ we prove that the stochastic current $\xi (x)$ is a Hida distribution. Moreover for $x=0\in {\mathbb{R}}^d$ with $d>1$ we show that the stochastic current is not a Hida distribution.

10 pages