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The lifetime of conditioned Brownian motion in planar domains of infinite area
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  • Published: December 1991

The lifetime of conditioned Brownian motion in planar domains of infinite area

  • Jianming Xu1 

Probability Theory and Related Fields volume 87, pages 469–487 (1991)Cite this article

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  • 11 Citations

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Summary

In this paper, it is shown that all expected lifetimes ofh-processes inD are finite if and only if the area ofD is finite ifD={(x,y):ø_(x)>y<ø+(x), − ∞<x<∞}, where ø_(x)<ø+ are two Lipschitz functions. We show that if Ω is a bounded convex region in the plane, there is anh-process in Ω with expected lifetime at leastc area (Ω). We also give an example of a planar domainD of infinite area such that the expected lifetime of eachh-process inD is finite.

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Authors and Affiliations

  1. Department of Mathematics, Purdue University, 47907, West Lafayette, IN, USA

    Jianming Xu

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  1. Jianming Xu
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Cite this article

Xu, J. The lifetime of conditioned Brownian motion in planar domains of infinite area. Probab. Th. Rel. Fields 87, 469–487 (1991). https://doi.org/10.1007/BF01304276

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  • Received: 03 January 1990

  • Revised: 05 July 1990

  • Issue Date: December 1991

  • DOI: https://doi.org/10.1007/BF01304276

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Keywords

  • Stochastic Process
  • Brownian Motion
  • Probability Theory
  • Mathematical Biology
  • Lipschitz Function
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