A White Noise Approach to Occupation Times of Brownian Motion

Occupation times of a stochastic process models the amount time spends inside spatial interval during certain finite horizon. It appears in fiber lay-down nonwoven production industry. The occupation can be interpreted as mass material deposited some region. From application point view, it is important to know average per unit area final fleece. In this paper we use white noise theory prove existence one-dimensional Brownian motion and provide an expression for expected value times.