The lifetime of conditioned Brownian motion in certain Lipschitz domains
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.
series expansion for the distribution of the lifetime
scientific article; zbMATH DE number 3951734
scientific article