Expected Value of the Occupation Times of Brownian Motion

Suryawan, Herry Pribawanto

International Journal of Applied Sciences and Smart Technologies
Volume 06, Issue 1, June 2024

Occupation times of a stochastic process describes the amount of time the process spends inside a spatial interval during a certain finite time horizon. It appears in the fiber lay-down process in nonwoven production industry. The occupation time can be interpreted as the mass of fiber material deposited inside some region.  From application point of view, it is important to know the average mass per unit area of the final fleece. In this paper derive an expression for the expected value of the occupation times in terms of Gaussian error functions.