Lifetimes of conditioned diffusions

Abstract

We investigate when an upper bound on expected lifetimes of conditioned diffusions associated with elliptic operators in divergence and non-divergence form can be found. The critical value of the parameter is found for each of the following classes of domains: L [to the power of p] domains (p = n − 1), uniformly regular twisted L [to the power of p] domains (p = n − 1), and twisted Hölder domains ([alpha] = 1/3). A related parabolic boundary Harnack principle is proved.