Induced Dirichlet Forms and Capacitary Inequalities

Abstract

A Dirichlet form on a large (complicated or multidimensional) space may be carried over onto a small (simple or one-dimensional) space. Here conditions are given ensuring the induced form is regular. A capacitary inequality between the two forms allows one to estimate the probability of a large deviation on the large space by that on the small space. Also asymptotically sharp results are derived in a one-dimensional setting.