The Stochastic Neural Field Equation with discontinuous firing rate

23.06.2015, 15:00-15:45  –  Am Neuen Palais, Haus 22 Raum 1.27
Forschungsseminar Wahrscheinlichkeitstheorie

Jennifer Krüger (Berlin)

In this talk we will discuss the existence and uniqueness of solutions to the stochastic neural field equation with Heaviside firing rate, which can be categorized as a nonlocal (stochastic) differential equation with discontinuous nonlinearity. We will construct mild solutions of the deterministic as well as for the stochastic field equation by a

fixed-point iteration and will then see that in the deterministic setting uniqueness fails to hold for a certain class of initial conditions.