Stochastic chains with long memory

• Grant number: 15/09094-3
• Support type: Regular Research Grants
• Duration: July 01, 2015 - June 30, 2017
• Field of knowledge: Physical Sciences and Mathematics - Probability and Statistics - Probability
• Principal Investigator: Alexsandro Giacomo Grimbert Gallo
• Grantee: Alexsandro Giacomo Grimbert Gallo
• Home Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil
• Assoc. researchers: Ricardo Felipe Ferreira

Abstract

We propose to develop a general study of long range stochastic chains, under several approaches listed below.(1) Questions related to existence and uniqueness of the stationary measure. (2) Construction of algorithms that perfectly simulates the stationary measure, and relation with the notion of finitary coding. (3) Relation between the notion of Gibbsianess and the notion of regularity of a stochastic chain. (4) Statistical inference of some characteristics of these chains. So this project is at the intersection of several areas of research (stochastic processes, dynamical systems, statistical physics, statistical inference), all related to the actual development of the theory of probabilities. (AU)

Scientific publications

(5)

(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; GARCIA, NANCY L. Discrete One-Dimensional Coverage Process on a Renewal Process. Journal of Statistical Physics, v. 173, n. 2, p. 381-397, OCT 2018. Web of Science Citations: 0.

GALLO, SANDRO; RODRIGUEZ, PABLO M. FROG MODELS ON TREES THROUGH RENEWAL THEORY. JOURNAL OF APPLIED PROBABILITY, v. 55, n. 3, p. 887-899, SEP 2018. Web of Science Citations: 1.

ABADI, MIGUEL; GALLO, SANDRO; RADA-MORA, ERIKA ALEJANDRA. The Shortest Possible Return Time of ss-Mixing Processes. IEEE TRANSACTIONS ON INFORMATION THEORY, v. 64, n. 7, p. 4895-4906, JUL 2018. Web of Science Citations: 1.

GALLESCO, CHRISTOPHE; GALLO, SANDRO; TAKAHASHI, DANIEL Y. Dynamic uniqueness for stochastic chains with unbounded memory. Stochastic Processes and their Applications, v. 128, n. 2, p. 689-706, FEB 2018. Web of Science Citations: 2.

GALLO, SANDRO; LEONARDI, FLORENCIA. Nonparametric statistical inference for the context tree of a stationary ergodic process. ELECTRONIC JOURNAL OF STATISTICS, v. 9, n. 2, p. 2076-2098, 2015. Web of Science Citations: 0.