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Large deviations principle for stochastic processes

Grant number: 17/20482-0
Support Opportunities:Research Grants - Visiting Researcher Grant - International
Duration: April 23, 2018 - October 22, 2018
Field of knowledge:Physical Sciences and Mathematics - Probability and Statistics - Probability
Principal Investigator:Anatoli Iambartsev
Grantee:Anatoli Iambartsev
Visiting researcher: Logachev Artem
Visiting researcher institution: Siberian Branch of the Russian Academy of Sciences (SB RAS), Russia
Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
Associated research grant:17/10555-0 - Stochastic modeling of interacting systems, AP.TEM

Abstract

The project originated from our joint work on the large deviations for the famous birth-death processes. Some generalizations of the obtained results is one of the goals of this project. We also want to understand how the form of the rate function changes depending on an asymptotic behavior of intensities of the process. Recent works and discussions about large deviations for Markov processes lead us to an ideia to include and develop in the project an alternative, to the Feng & Kurtz large deviation program, and more simple way of proving the large deviations for Markov processes and functionals of them. (AU)

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Scientific publications (4)
(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)
LOGACHOV, ARTEM; LOGACHOVA, OLGA; YAMBARTSEV, ANATOLY. The local principle of large deviations for compound Poisson process with catastrophes. BRAZILIAN JOURNAL OF PROBABILITY AND STATISTICS, v. 35, n. 2, p. 205-223, . (17/10555-0, 17/20482-0)
LOGACHOV, A.; LOGACHOVA, O.; YAMBARTSEV, A.. Large deviations in a population dynamics with catastrophes. Statistics & Probability Letters, v. 149, p. 29-37, . (17/20482-0, 17/10555-0)
LOGACHOV, A.; MOGULSKII, A.; YAMBARTSEV, A.. imit theorems for chains with unbounded variable length memory which satisfy Cramer condition{*. ESAIM-PROBABILITY AND STATISTICS, v. 26, p. 152-170, . (17/10555-0, 13/07699-0, 17/20482-0)
LOGACHOV, A.; LOGACHOVA, O.; YAMBARTSEV, A.. Local large deviation principle for Wiener process with random resetting. Stochastics and Dynamics, v. 20, n. 5, . (17/20482-0, 17/10555-0)

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