GIBBS POINT PROCESS APPROXIMATION: TOTAL VARIATION BOUNDS USING STEIN'S METHOD
成果类型：
Article
署名作者：
Schuhmacher, Dominic; Stucki, Kaspar
署名单位：
University of Bern; University of Gottingen
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
DOI：
10.1214/13-AOP895
发表日期：
2014
页码：
1911-1951
关键词：
摘要：
We obtain upper bounds for the total variation distance between the distributions of two Gibbs point processes in a very general setting. Applications are provided to various well-known processes and settings from spatial statistics and statistical physics, including the comparison of two Lennard-Jones processes, hard core approximation of an area interaction process and the approximation of lattice processes by a continuous Gibbs process. Our proof of the main results is based on Stein's method. We construct an explicit coupling between two spatial birth-death processes to obtain Stein factors, and employ the Georgii-Nguyen-Zessin equation for the total bound.