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
where λ D is the first eigenvalue of 1/2 Δ on D.
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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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DOI: https://doi.org/10.1007/BF00320080