Probability Theory and Related Fields

, Volume 75, Issue 1, pp 55–65

The lifetime of conditioned Brownian motion in certain Lipschitz domains

  • R. Dante DeBlassie
Article

DOI: 10.1007/BF00320080

Cite this article as:
DeBlassie, R.D. Probab. Th. Rel. Fields (1987) 75: 55. doi:10.1007/BF00320080

Summary

For certain Lipschitz domains D we obtain a series expansion for the distribution of the lifetime τD 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 λD is the first eigenvalue of 1/2 Δ on D.

Copyright information

© Springer-Verlag 1987

Authors and Affiliations

  • R. Dante DeBlassie
    • 1
  1. 1.Department of MathematicsTexas A&M UniversityCollege StationUSA