Abstract

Abstract. We develop exact random variate generators for several distributions related to the Jacobi theta function. These include the distributions of the maximum of a Brownian bridge, a Brownian meander and a Brownian excursion, and distributions of certain first passage times of Bessel processes. The algorithms are based on the alternating series method. Furthermore, we survey various distributional identities and point out ways of dealing with generalizations of these basic distributions. Keywords and phrases. Random variate generation. Stable distribution. First passage time. Brownian motion. Rejection method. Simulation. Monte Carlo method. Expected time analysis. Probability inequalities.

Citations