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

• Grant number: 16/17789-4
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: December 01, 2016
• End date: February 28, 2018
• Field of knowledge: Physical Sciences and Mathematics - Probability and Statistics - Probability
• Principal Investigator: Pablo Augusto Ferrari
• Grantee: Guilherme Ost de Aguiar
• Host 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

Abstract

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

(5)

(The scientific publications listed on this page originate from the Web of Science or SciELO databases. Their authors have cited FAPESP grant or fellowship project numbers awarded to Principal Investigators or Fellowship Recipients, whether or not they are among the authors. This information is collected automatically and retrieved directly from those bibliometric databases.)

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. (16/17791-9, 13/07699-0, 16/17789-4)

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. (16/17791-9, 13/07699-0, 16/17789-4)

HERNANDEZ, NOSLEN; DUARTE, ALINE; OST, GUILHERME; FRAIMAN, RICARDO; GALVES, ANTONIO; VARGAS, CLAUDIA D.. Retrieving the structure of probabilistic sequences of auditory stimuli from EEG data. SCIENTIFIC REPORTS, v. 11, n. 1, FEB 10 2021. (16/22053-7, 13/07699-0, 16/17791-9, 16/17789-4)

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. (13/07699-0, 16/17791-9, 16/17789-4)

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. (16/17791-9, 13/07699-0, 16/17789-4)