Special Session 191: Stochastic Dynamical Systems Under Levy Noise: Theory and Applications

Anomalous branching processes: probabilistic behavior and connection to nonlinear time-fractional PDEs
Nicolas Privault
Nanyang Technological University
Singapore
Co-Author(s):    Gerardo Perez-Suarez and Nicolas Privault
Abstract:
We present a class of non-Markovian branching processes, called anomalous branching processes, and study their probabilistic properties, such as the behavior of the moments of the number of particles alive at a time t on a given set. Those processes are then used to derive a probabilistic representation for the solutions of time-fractional F-KPP equations. By exploiting this connection, we also derive estimates for the probability tail of the position of the rightmost particle in the one-dimensional case.