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 γ > 0, a “typical” increment of a reflecting historical path over a small time interval Δt is not greater than (Δt)3/4−γ.
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Received: 16 March 2000 / Revised version: 26 February 2001 / Published online: 9 October 2001
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Burdzy, K., Le Gall, JF. Super-Brownian motion with reflecting historical paths. Probab Theory Relat Fields 121, 447–491 (2001). https://doi.org/10.1007/s004400100157
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DOI: https://doi.org/10.1007/s004400100157
Keywords
- Small Time
- Limit Distribution
- Discrete Approximation
- Historical Path
- Path Behavior