Poincaré recurrence statistics and extreme value theory

• Grant number: 17/07084-6
• Support Opportunities: Scholarships abroad - Research
• Start date: July 23, 2017
• End date: July 22, 2018
• Field of knowledge: Physical Sciences and Mathematics - Probability and Statistics - Probability
• Principal Investigator: Alexsandro Giacomo Grimbert Gallo
• Grantee: Alexsandro Giacomo Grimbert Gallo
• Host Investigator: Sandro Vaienti
• Host Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil
• Institution abroad: Centre de Physique Théorique (CPT), France

Abstract

The main objective of the present project is to study the Poincaré recurrence statistics, and their relations with extreme value theory, for stochastic processes (or equivalently, dynamical systems). Our focus will be through a statistics of the process called first possible return time. First, we want to study the asymptotic properties of the first possible return time, under general conditions for the stochastic processes. Next, we will explore the relation between the first possible return time and the so-called ''extremal index'', which quantifies the intensity of clustering of exceedance in the process. (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.)

ABADI, M.; AMORIM, V; CHAZOTTES, J-R; GALLO, S.. Return-time L-q-spectrum for equilibrium states with potentials of summable variation. Ergodic Theory and Dynamical Systems, v. N/A, p. 27-pg., 2022-06-06. (17/07084-6)

GALLO, SANDRO; HAYDN, NICOLAI; VAIENTI, SANDRO. Number of visits in arbitrary sets for 0-mixing dynamics. ANNALES DE L INSTITUT HENRI POINCARE-PROBABILITES ET STATISTIQUES, v. 60, n. 2, p. 38-pg., 2024-05-01. (13/07699-0, 17/07084-6, 19/23439-4)

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. (14/26419-0, 17/07084-6, 15/09094-3, 13/07699-0)

FERREIRA, RICARDO F.; GALLO, SANDRO; PACCAUT, FREDERIC. Non-regularg-measures and variable length memory chains. Nonlinearity, v. 33, n. 11, p. 27-pg., 2020-11-01. (16/12918-0, 17/07084-6)

CHAZOTTES, JEAN-RENE; GALLO, SANDRO; TAKAHASHI, DANIEL Y.. GAUSSIAN CONCENTRATION BOUNDS FOR STOCHASTIC CHAINS OF UNBOUNDED MEMORY. ANNALS OF APPLIED PROBABILITY, v. 33, n. 5, p. 30-pg., 2023-10-01. (17/07084-6, 19/23439-4)