  Stochastic homogenization is achieved for a class of elliptic and parabolic
equations describing the lifetime, in large domains, of stationary diffusion
processes in random environment which are small, statistically isotropic
perturbations of Brownian motion in dimension at least three. Furthermore, the
homogenization is shown to occur with an algebraic rate. Such processes were
first considered in the continuous setting by Sznitman and Zeitouni [21], upon
whose results the present work relies strongly, and more recently their
smoothed exit distributions from large domains were shown to converge to those
of a Brownian motion by the author [10]. This work shares in philosophy with
[10], but requires substantially new methods in order to control the
expectation of exit times which are generically unbounded in the microscopic
scale due to the emergence of a singular drift in the asymptotic limit.
