  In this monograph, we prove an asymptotic approximation for integrals of
probability densities over sets in finite dimensional euclidean space, which
are far away from the origin (asymptotic sets). We use this approximation to
investigate tails of quadratic forms of random vectors, supremum of random
linear forms among others. Applications to the study of finite size random
matrices, finite sample statistics of autoregressive processes, and supremum of
some stochastic processes.
