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On exact simulation algorithms for some distributions related to Jacobi theta functions

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  • Devroye, Luc

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.

Suggested Citation

  • Devroye, Luc, 2009. "On exact simulation algorithms for some distributions related to Jacobi theta functions," Statistics & Probability Letters, Elsevier, vol. 79(21), pages 2251-2259, November.
    • Handle: RePEc:eee:stapro:v:79:y:2009:i:21:p:2251-2259
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    References listed on IDEAS

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    1. Devroye, Luc, 1997. "Simulating theta random variates," Statistics & Probability Letters, Elsevier, vol. 31(4), pages 275-279, February.
    2. Burq, Zaeem A. & Jones, Owen D., 2008. "Simulation of Brownian motion at first-passage times," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 77(1), pages 64-71.
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    Cited by:

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