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The lifetime of conditioned Brownian motion in certain Lipschitz domains
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  • Published: May 1987

The lifetime of conditioned Brownian motion in certain Lipschitz domains

  • R. Dante DeBlassie1 

Probability Theory and Related Fields volume 75, pages 55–65 (1987)Cite this article

Summary

For certain Lipschitz domains D we obtain a series expansion for the distribution of the lifetime τ D of conditioned Brownian motion on D. From this we determine

$$\mathop {lim}\limits_{t \to \infty } {\text{ }}t^{ - 1} {\text{ }}log{\text{ }}P_x^h (\tau _D {\text{ > }}t) = \mathop {lim}\limits_{t \to \infty } {\text{ }}t^{ - 1} {\text{ }}log{\text{ }}P_x (\tau _D {\text{ > }}t) = {\text{--}}\lambda _D {\text{,}}$$

where λ D is the first eigenvalue of 1/2 Δ on D.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Texas A&M University, 77843, College Station, TX, USA

    R. Dante DeBlassie

Authors
  1. R. Dante DeBlassie
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Additional information

Supported in part by the National Science Foundation under grant DMS-830167

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DeBlassie, R.D. The lifetime of conditioned Brownian motion in certain Lipschitz domains. Probab. Th. Rel. Fields 75, 55–65 (1987). https://doi.org/10.1007/BF00320080

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  • Received: 08 November 1985

  • Issue Date: May 1987

  • DOI: https://doi.org/10.1007/BF00320080

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Keywords

  • Stochastic Process
  • Brownian Motion
  • Probability Theory
  • Series Expansion
  • Statistical Theory
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