Catastrophe Models: Binomial, Uniform, and Geometric

• Grant number: 25/03804-0
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: August 01, 2025
• End date: July 31, 2027
• Field of knowledge: Physical Sciences and Mathematics - Probability and Statistics - Probability
• Principal Investigator: Fabio Prates Machado
• Grantee: Jose Hermenegildo Ramirez Gonzalez
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Associated research grant: 23/13453-5 - Stochastic systems modeling, AP.TEM

Abstract

This research focuses on the development of stochastic models in population dynamics, with an emphasis on branching particle systems, stochastic growth mechanisms, and processes subject to catastrophes and immigration. These models provide a rigorous mathematical framework for studying population evolution under random fluctuations, where extinction, dispersion, and long-term persistence depend on underlying stochastic interactions. The analysis of asymptotic behaviors, occupation times, and scaling limits allows for a deeper understanding of the mechanisms governing population variability and stability.An essential component of this work is the study of branching particle systems, in which individuals evolve according to random movement, lifetimes, and reproduction mechanisms. These systems offer insights into convergence to nontrivial populations, conditions for local extinction, occupation times, among other aspects. In addition to theoretical advances, this research connects to applications in real-world stochastic systems, particularly in animal telemetry and population growth. (AU)