Displaying similar documents to “A probabilistic approach to the trace at the boundary for solutions of a semilinear parabolic partial differential equation.”

Hitting probabilities and potential theory for the brownian path-valued process

Jean-François Le Gall (1994)

Annales de l'institut Fourier


We consider the Brownian path-valued process studied in [LG1], [LG2], which is closely related to super Brownian motion. We obtain several potential-theoretic results related to this process. In particular, we give an explicit description of the capacitary distribution of certain subsets of the path space, such as the set of paths that hit a given closed set. These capacitary distributions are characterized as the laws of solutions of certain stochastic differential equations. They solve...