Abstract.
We prove that the sequence of finite reflecting branching Brownian motion forests defined by Burdzy and Le Gall ([1]) converges in probability to the “super-Brownian motion with reflecting historical paths.” This solves an open problem posed in [1], where only tightness was proved for the sequence of approximations. Several results on path behavior were proved in [1] for all subsequential limits–they obviously hold for the unique limit found in the present paper.
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Mathematics Subject Classification (2000): Primary 60H15, Secondary 35R60
Supported in part by NSF Grant DMS-0071486, Israel Science Foundation Grants 12/98 and 116/01 - 10.0, and the U.S.-Israel Binational Science Foundation (grant No. 2000065).
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Burdzy, K., Mytnik, L. Super-Brownian motion with reflecting historical paths. II. Convergence of approximations. Probab. Theory Relat. Fields 133, 145–174 (2005). https://doi.org/10.1007/s00440-004-0413-4
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DOI: https://doi.org/10.1007/s00440-004-0413-4
Keywords
- Super-Brownian motion
- Reflecting paths
- Brownian snake
- Martingale problem