Stochastic integral representation and regularity of the density for the exit measure of super-Brownian motion
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Publication:2497213
DOI10.1214/009117904000000612zbMATH Open1097.60033arXivmath/0503599OpenAlexW2166020101MaRDI QIDQ2497213
Author name not available (Why is that?)
Publication date: 3 August 2006
Published in: (Search for Journal in Brave)
Abstract: This paper studies the regularity properties of the density of the exit measure for super-Brownian motion with (1+�eta)-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 Delta u=u^{1+�eta}.
Full work available at URL: https://arxiv.org/abs/math/0503599
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