Approximation of integrals over asymptotic sets with applications to probability and statistics

Details Approximation of integrals over asymptotic sets with applications to probability and statistics Approximation of integrals over asymptotic sets with applications to probability and statistics

2003-12-05

arxiv.org/abs/math/0312132v1

Mathematics

Probability

315 pages; some stereoscopic pictures

Scientific paper

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.

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