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Stochastic integral representation and regularity of the density for the Exit measure of super-Brownian motion

Jean-Francois Le Gall·Leonid Mytnik
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Abstract

This paper studies the regularity properties of the density of the exit measure for super-Brownian motion with (1+β)-stable branching mechanism. It establishes the continuity of the density in dimension d=2 and the unboundedness of the density in all other dimensions where the density exists. An alternative description of the exit measure and its density is also given via a stochastic integral representation. Results are applied to the probabilistic representation of nonnegative solutions of the partial differential equation Δu=u^{1+β}.

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Jean-Francois Le Gall, Leonid Mytnik. 2005-03-25. Stochastic integral representation and regularity of the density for the Exit measure of super-Brownian motion. https://doi.org/10.1214/009117904000000612

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