The lifetime of conditioned Brownian motion in certain Lipschitz domains. (English) Zbl 0592.60068
For certain Lipschitz domains D we obtain a series expansion for the distribution of the lifetime \(\tau_ D\) of conditioned Brownian motion on D. From this we determine
\[
\lim_{t\to \infty}t^{-1} \log P^ h_ x(\tau_ D>t)=\lim_{t\to \infty}t^{-1}\quad \log P_ x(\tau_ D>t)=-\lambda_ D,
\]
where \(\lambda_ D\) is the first eigenvalue of \(\Delta\) /2 on D.
Keywords:
series expansion for the distribution of the lifetime; conditioned Brownian motion; first eigenvalueReferences:
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