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Stochastic processes with variable length memory: Monge-Kantorovich problem, bootstrap and particle systems

Grant number: 09/09809-1
Support Opportunities:Scholarships in Brazil - Post-Doctoral
Effective date (Start): November 01, 2009
Effective date (End): September 30, 2011
Field of knowledge:Physical Sciences and Mathematics - Probability and Statistics - Probability
Principal Investigator:Nancy Lopes Garcia
Grantee:Alexsandro Giacomo Grimbert Gallo
Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

This project contains two principal parts which can be seen as a continuation and generalization of the PhD Thesis of the candidate. First, we will use the regenerative structure of the stochastic processes with unbounded variable length memory which have been introduced in the PhD Thesis \citep{gallo/2009} to solve two questions of actual probability theory. The first one is the Monge-Kantorovich problem for stationary laws of infinite memory chains. The second is the use of the regeneration scheme as a base to perform bootstrap for sotchastic chains of infinite memory. In a second part, we would like to find new criteria ensuring the existence and uniqueness of the stationary law for markovian particle system with infinite range, and in particular, an alternative to the traditional continuity assumption \citep*{galves/garcia/eva/2009}. Such an alternative can also be found in the notion of processes with variable range. Hence, a natural way would be to extend the results of the PhD Thesis of the candidate on perfect simulation for stochastic chains with variable length memory to the case of particle systems with variable range. (AU)

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Scientific publications (8)
(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)
GALLO, SANDRO; TAKAHASHI, DANIEL Y.. Attractive regular stochastic chains: perfect simulation and phase transition. Ergodic Theory and Dynamical Systems, v. 34, n. 5, p. 1567-1586, . (09/09809-1, 08/08171-0)
GALLO, SANDRO; GARCIA, NANCY L.. Perfect simulation for locally continuous chains of infinite order. Stochastic Processes and their Applications, v. 123, n. 11, p. 3877-3902, . (09/09809-1)
FERNANDEZ, ROBERTO; GALLO, SANDRO; MAILLARD, GREGORY. REGULAR G-MEASURES ARE NOT ALWAYS GIBBSIAN. Electronic Communications in Probability, v. 16, p. 732-740, . (09/09809-1)
GALLO, SANDRO; TAKAHASHI, DANIEL Y.. Attractive regular stochastic chains: perfect simulation and phase transition. Ergodic Theory and Dynamical Systems, v. 34, p. 20-pg., . (09/09809-1, 08/08171-0)
GALLESCO, C.; GALLO, S.; TAKAHASHI, D. Y.. Explicit estimates in the Bramson-Kalikow model. Nonlinearity, v. 27, n. 9, p. 2281-2296, . (09/09809-1, 08/08171-0, 13/10101-9)
ABADI, MIGUEL; CARDENO, LILIAM; GALLO, SANDRO. Potential Well Spectrum and Hitting Time in Renewal Processes. Journal of Statistical Physics, v. 159, n. 5, p. 1087-1106, . (09/09809-1)
GALLO, S.; LERASLE, M.; TAKAHASHI, D. Y.. Markov Approximation of Chains of Infinite Order in the (d)over-bar-metric. Markov Processes and Related Fields, v. 19, n. 1, p. 51-82, . (09/09494-0, 09/09809-1, 08/08171-0)
GALLO, SANDRO; PACCAUT, FREDERIC. On non-regular g-measures. Nonlinearity, v. 26, n. 3, p. 763-776, . (09/09809-1)

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