Self-intersection local time derivative for systems of non-linear stochastic heat equations

Abstract

We consider the existence and Hölder continuity conditions for the higher-order derivative of self-intersection local time for u(t, x), where u(t,x)=u1(t,x),…,ud(t,x) is the solution to a system of non-linear stochastic heat equations driven by a d-dimensional space-time white noise. Moreover, we study the cases of intersection local time and collision local time.