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The h-path distribution of the lifetime of conditioned brownian motion for non-smooth domains
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  • Published: August 1989

The h-path distribution of the lifetime of conditioned brownian motion for non-smooth domains

  • Carlos E. Kenig1 &
  • Jill Pipher1 

Probability Theory and Related Fields volume 82, pages 615–623 (1989)Cite this article

Summary

Consider the h-paths of Doob, and let τD be the lifetime of Brownian motion killed at ∂D, where D is a bounded Lipschitz (or NTA) domain in ℝn. then,

$$\log P_x^h (\tau _D > t) \sim - \lambda _D t as t \to \infty $$

where λD is the first positive eigenvalue of-1/2Δ on D.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Chicago, 60637, Chicago, IL, USA

    Carlos E. Kenig & Jill Pipher

Authors
  1. Carlos E. Kenig
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  2. Jill Pipher
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Additional information

Supported in part by the NSF and the J.S. Guggenheim Foundation

Supported in part by an NSF Postdoctoral Fellowship

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Kenig, C.E., Pipher, J. The h-path distribution of the lifetime of conditioned brownian motion for non-smooth domains. Probab. Th. Rel. Fields 82, 615–623 (1989). https://doi.org/10.1007/BF00341286

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  • Received: 19 September 1987

  • Revised: 05 September 1988

  • Issue Date: August 1989

  • DOI: https://doi.org/10.1007/BF00341286

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Keywords

  • Stochastic Process
  • Brownian Motion
  • Probability Theory
  • Statistical Theory
  • Positive Eigenvalue
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