LAST EXIT DISTRIBUTIONS AND MAXIMUM EXCURSION FOR BROWNIAN MOTION

<正> This paper discusses the last exit time and place of a sphere, maximum excursion before lastexit and the time for first attaining the maximum. Distributions and moments of the above fourrandom variables are found. The properties of moments distinguish the Brownian motion in variousdimensions. In particular, it is shown that the distributions of last exit place and first hittingplace of a sphere with center 0 are the same, i.e, the uniform distribution on the sphere, if X0 = 0.