Brownian cuboid and its geometric characteristics

摘要

A class of random cuboid model which is defined Brownian cuboid is constructed in this paper. Based on the structure characteristics of Brownian cuboid and the properties of Brownian motion, geometric characteristics of Brownian cuboid are discussed, by which the probability estimates of the length of the space diagonal, surface area and volume are obtained, and moreover, the small deviation estimates and some relevant results for the geometric characteristics of Brownian cuboid are given. Additionally, we directly derive the upper and lower bounds for the smallest positive zero of the Bessel functions of the first kind.