A Lemma on Super-Brownian Motion with Some Applications
We prove a lemma concerning the behavior of the historical paths of super-Brownian motion near their endpoint. We use this lemma to estimate the hitting probability of a small disk for two-dimensional super-Brownian motion, thus complementing results due to Dawson, Iscoe and Perkins  in higher dimensions. These estimates are related to the large time behavior of the solutions of a semilinear parabolic equation, which has been investigated by several authors using analytic methods.
KeywordsBrownian Motion Strong Markov Property Positive Excursion Historical Path Trivial Path
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