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Stability, statistical selection of models and hydrodynamic boundary for interacting chains with variable reach memory

Grant number: 16/17789-4
Support type:Scholarships in Brazil - Post-Doctorate
Effective date (Start): December 01, 2016
Effective date (End): February 28, 2018
Field of knowledge:Physical Sciences and Mathematics - Probability and Statistics - Probability
Principal Investigator:Pablo Augusto Ferrari
Grantee:Guilherme Ost de Aguiar
Home Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
Associated research grant:13/07699-0 - Research, Innovation and Dissemination Center for Neuromathematics - NeuroMat, AP.CEPID


My research has been mostly focused on statistical model selection for systems of discrete time interacting chains with memory of variable length introduced by Galves-Löcherbach recentlyas well as on stability properties and hydrodynamic limits for their continuous timecounterparts. In this research proposal we present some results recently achievedand address future challenges for research within the mission of the research centerNeuroMat which we intend to investigate. (AU)

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)
DUARTE, ALINE; LOCHERBACH, EVA; OST, GUILHERME. Stability, convergence to equilibrium and simulation of non-linear Hawkes processes with memory kernels given by the sum of Erlang kernels. ESAIM-PROBABILITY AND STATISTICS, v. 23, p. 770-796, DEC 20 2019. Web of Science Citations: 0.
DUARTE, ALINE; FRAIMAN, RICARDO; GALVES, ANTONIO; OST, GUILHERME; VARGAS, CLAUDIA D. Retrieving a Context Tree from EEG Data. MATHEMATICS, v. 7, n. 5 MAY 2019. Web of Science Citations: 0.
DUARTE, ALINE; GALVES, ANTONIO; LOCHERBACH, EVA; OST, GUILHERME. Estimating the interaction graph of stochastic neural dynamics. BERNOULLI, v. 25, n. 1, p. 771-792, FEB 2019. Web of Science Citations: 0.
CHEVALLIER, J.; DUARTE, A.; LOCHERBACH, E.; OST, G. Mean field limits for nonlinear spatially extended Hawkes processes with exponential memory kernels. Stochastic Processes and their Applications, v. 129, n. 1, p. 1-27, JAN 2019. Web of Science Citations: 2.

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