, Volume 83, Issue 1-2, pp 135-205

Super-Brownian motion: Path properties and hitting probabilities

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Summary

Sample path properties of super-Brownian motion including a one-sided modulus of continuity and exact Hausdorff measure function of the range and closed support are obtained. Analytic estimates for the probability of hitting balls lead to upper bounds on the Hausdorff measure of the set of k-multiple points and a sufficient condition for a set to be “polar”.

Dedicated to Klaus Krickeberg on the occasion of his 60th birthday
Research partially supported by a Natural Sciences and Engineering Research Council of Canada operating grant