Brownian motion and Box-Muller transformation

Linfeng Zhang

doi:10.1117/12.2628103

22 April 2022 Brownian motion and Box-Muller transformation

Linfeng Zhang

Proceedings Volume 12163, International Conference on Statistics, Applied Mathematics, and Computing Science (CSAMCS 2021); 121633Z (2022) https://doi.org/10.1117/12.2628103
Event: International Conference on Statistics, Applied Mathematics, and Computing Science (CSAMCS 2021), 2021, Nanjing, China

Abstract

An important capacity for modeling across a wide-ranging area is the rapid creation of high-quality Gaussian random numbers (GRNs). Advances in computation have given us the ability to run replications with very huge amounts of accidental numbers, but they've also given us the problem of satisfying ever-higher standards for the quality of GRN generators. In this paper, the importance of high-quality generation of Gaussian random variables (GRV) is revealed by detailed proof of properties of Brownian motion (BM). Several important properties regarding geometric BM are also discussed. The method of Box-Muller transformation for generation of Gaussian variables is discussed.

Citation Download Citation

Linfeng Zhang "Brownian motion and Box-Muller transformation", Proc. SPIE 12163, International Conference on Statistics, Applied Mathematics, and Computing Science (CSAMCS 2021), 121633Z (22 April 2022); https://doi.org/10.1117/12.2628103

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