Convex Hull of Brownian Motion and Brownian Bridge
S. Sebek
2024, v.30, Issue 4, 459-475
ABSTRACT
In this article we study the convex hull spanned by the union of trajectories of a standard planar Brownian motion, and an independent standard planar Brownian bridge. We find the exact values of the expectation of perimeter and area of such a convex hull. As an auxiliary result, that is of interest in its own right, we provide an explicit shape of the probability density function of a random variable that represents the time when the combined maximum of a standard one-dimensional Brownian motion, and an independent standard one-dimensional Brownian bridge is attained. At the end, we generalize our results to the case of multiple independent standard planar Brownian motions and Brownian bridges.
Keywords: convex hull, Brownian motion, Brownian bridge, area, perimeter
COMMENTS
Please log in or register to leave a comment