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Super-Brownian motion with reflecting historical paths

Authors
  • Burdzy, Krzysztof
  • Gall, Jean-Francois Le
Type
Preprint
Publication Date
Mar 09, 2000
Submission Date
Mar 09, 2000
Identifiers
arXiv ID: math/0003056
Source
arXiv
License
Unknown
External links

Abstract

We consider super-Brownian motion whose historical paths reflect from each other, unlike those of the usual historical super-Brownian motion. We prove tightness for the family of distributions corresponding to a sequence of discrete approximations but we leave the problem of uniqueness of the limit open. We prove a few results about path behavior for processes under any limit distribution. In particular, we show that for any $\gamma>0$, a "typical" increment of a reflecting historical path over a small time interval $\Delta t$ is not greater than $(\Delta t)^{3/4 - \gamma}$.

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