Coupling and comparison between local time fields of Markov chains and of sequences of independent and identically distributed random variables

• Grant number: 16/13646-4
• Support Opportunities: Regular Research Grants
• Start date: September 01, 2016
• End date: August 31, 2017
• Field of knowledge: Physical Sciences and Mathematics - Probability and Statistics - Probability
• Principal Investigator: Diego Fernando de Bernardini
• Grantee: Diego Fernando de Bernardini
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

In this research project we propose to investigate originally the problem of the comparison between the random fields of local times of a Markov chain which has a unique invariant probability measure and of a sequence of independent and identically distributed random variables with probability law given by the invariant measure of the chain, up to a specific moment, by studying the total variation distance between the laws of these random fields. To do so, we intend to obtain a coupling between the local times fields of the two mentioned processes, up to a given moment, using the technique of soft local times. As a consequence, we hope to obtain an upper bound for the refered total variation distance between the fields, which we expect to be reasonable and interesting under certain assumptions, and also small for a broad and important class of Markov chains involving such assumptions. (AU)

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

DE BERNARDINI, DIEGO F.; GALLESCO, CHRISTOPHE; POPOV, SERGUEI. On uniform closeness of local times of Markov chains and i.i.d. sequences. Stochastic Processes and their Applications, v. 128, n. 10, p. 3221-3252, OCT 2018. (16/13646-4, 17/02022-2)