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,
where λD is the first positive eigenvalue of-1/2Δ on D.
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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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DOI: https://doi.org/10.1007/BF00341286
Keywords
- Stochastic Process
- Brownian Motion
- Probability Theory
- Statistical Theory
- Positive Eigenvalue