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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 type:Regular Research Grants
Duration: September 01, 2016 - August 31, 2017
Field of knowledge:Physical Sciences and Mathematics - Probability and Statistics
Principal Investigator:Diego Fernando de Bernardini
Grantee:Diego Fernando de Bernardini
Home Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil


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. Web of Science Citations: 1.

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