Exit Measures and the Nonlinear Dirichlet Problem
Jean‐François Le Gall · Birkhäuser Basel eBooks · 1999
In this chapter we use the Brownian snake approach of the previous chapter to construct the exit measure of quadratic superprocesses. In the special case where the spatial motion is Brownian motion in ℝ d , the exit measure yields a probabilistic solution of the Dirichlet problem associated with the equation Δu = u2 in a regular domain. This probabilistic solution plays a major role in further developments that will be presented in the following chapters.