English

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

Probability 2009-09-29 v1 Classical Analysis and ODEs Statistics Theory Statistics Theory

Abstract

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.

Keywords

Cite

@article{arxiv.math/0312132,
  title  = {Approximation of integrals over asymptotic sets with applications to probability and statistics},
  author = {Philippe Barbe},
  journal= {arXiv preprint arXiv:math/0312132},
  year   = {2009}
}

Comments

315 pages; some stereoscopic pictures

R2 v1 2026-07-22T17:00:28.981Z