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Asymptotic Variance Parameters for the Boundary Local Times of Reflected Brownian Motion on a Compact Interval

R. Williams
Journal / Anthology

Journal of Applied Probability
Year: 1992
Volume: 29
Page range: 996-1002

A direct derivation is given of a formula for the normalized asymptotic variance parameters of the boundary local times of relected Brownian motion (with drift) on a compact interval. This formula was previously obtained by Berger and Whitt using and M/M/1/C queue approximation to the reflected Brownian motion. The bivariate Laplace transform of the hitting time of a level and the boundary local time up to that hitting time, for a one-dimensional reflected Brownian motion with drift, is obtained as part of the derivation.

*Mathematics > Probability and Statistics