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A ratio limit theorem for erased branching Brownian motion

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  • Salminen, Paavo

Abstract

In this paper we study a branching Brownian motion inside a bounded, smooth domain with killing at the boundary. The paths of the process are transformed--roughly speaking--so that all the branches which reach the boundary are totally erased with unit speed for a given time [rho], 0[less-than-or-equals, slant][rho][less-than-or-equals, slant][infinity], starting from the tip of the branch. A limit theorem for the ratio of the number of particles in the erased process and the original one is proved. This may be viewed as a generalisation of a result for Galton-Watson processes due to Athreya and Ney (1972).

Suggested Citation

  • Salminen, Paavo, 1992. "A ratio limit theorem for erased branching Brownian motion," Stochastic Processes and their Applications, Elsevier, vol. 41(2), pages 215-222, June.
    • Handle: RePEc:eee:spapps:v:41:y:1992:i:2:p:215-222
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