Simulating Nonstationary Spatio-Temporal Poisson Processes using the Inversion Method

24 Pages Posted: 20 Oct 2020

See all articles by Haoting Zhang

Haoting Zhang

University of California, Berkeley - Department of Industrial Engineering and Operations Research

Zeyu Zheng

University of California, Berkeley

Date Written: July 27, 2020

Abstract

We study the problem of simulating a class of nonstationary spatio-temporal Poisson processes. The Poisson intensity function is non-stationary and piecewise linear in both the time dimension and the spatial location dimensions. We propose an exact simulation algorithm based on the inversion method. This simulation algorithm adopts three advantages. First, the entire procedure involves only closed-form computation with no need for numerical integration or numerical inversion of any function. Each step in the algorithm only requires exact arithmetic operations. Second, the proposed algorithm is sample efficient, especially compared to the thinning method when the maximum intensity value is much larger than the minimum intensity value. Third, the algorithm generates arrivals sequentially, one at a time in ascending order, so that they can be conveniently fed into real-time or online decision-making tools.

Suggested Citation

Zhang, Haoting and Zheng, Zeyu, Simulating Nonstationary Spatio-Temporal Poisson Processes using the Inversion Method (July 27, 2020). Available at SSRN: https://ssrn.com/abstract=3661101 or http://dx.doi.org/10.2139/ssrn.3661101

Haoting Zhang (Contact Author)

University of California, Berkeley - Department of Industrial Engineering and Operations Research ( email )

4141 Etcheverry Hall
Berkeley, CA 94720-1777
United States

Zeyu Zheng

University of California, Berkeley ( email )

4125 Etcheverry Hall
Berkeley, CA 94720
United States

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