Stochastic chains with unbounded memory: statistical properties and applications

• Grant number: 25/00805-6
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: May 01, 2025
• End date: February 29, 2028
• Field of knowledge: Physical Sciences and Mathematics - Probability and Statistics - Probability
• Principal Investigator: Alexsandro Giacomo Grimbert Gallo
• Grantee: Vicenzo Bonasorte Reis Pereira
• Host Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil
• Associated research grant: 23/13453-5 - Stochastic systems modeling, AP.TEM

Abstract

Long range dependence arises widely in applied as well as theoretical problems. In this project, we propose an approach for stochastic chains with unbounded memory based on these two parts. First, a study of the basic statistical/theoretical properties (central limit theorem, concentration inequalities,perfect simulation algorithms, quasi-stationary distribution) and second a studyof two problems involving these objects: one model of propagation of information in dynamical random graphs and a percolation model on regular trees.