Extinction and survival of branching processes in varying environment

• Grant number: 17/17399-4
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: November 01, 2017
• End date: October 31, 2018
• Field of knowledge: Physical Sciences and Mathematics - Probability and Statistics - Probability
• Principal Investigator: Pablo Martin Rodriguez
• Grantee: Luna Wagner Cunha
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• Associated research grant: 13/07375-0 - CeMEAI - Center for Mathematical Sciences Applied to Industry, AP.CEPID

Abstract

The branching process, or Galton-Watson process, is a stochastic process with applications in fields like Biology, Physics, Computer Sciences, and others. In this project we will study the basic properties of this theory, and we will review the existing results about branching process in varying environment. This will be accomplished by comparing the existing results regarding the extinction of survival of such processes, and by showing examples and counter-examples in order to compare them. Also, we will discuss some applications. (AU)