# On asymptotics of multivariate integrals with applications to records

### Details

Serval ID

serval:BIB_0696E30FDCCA

Type

**Article**: article from journal or magazin.

Collection

Publications

Fund

Title

On asymptotics of multivariate integrals with applications to records

Journal

Stochastic Models

ISSN

1532-6349

1532-4214 ([electronic])

1532-4214 ([electronic])

Publication state

Published

Issued date

2002

Peer-reviewed

Oui

Volume

18

Number

1

Pages

41-69

Language

english

Abstract

Let {X-n,n greater than or equal to 1} be a sequence of iid. Gaussian random vectors in R-d, d greater than or equal to 2, with nonsingular distribution function F. In this paper the asymptotics for the sequence of integrals I-F,I-n(G(n)) := n integral(Rd)G(n)(n-1)(X) dF(X) is considered with G(n) some distribution function on R-d. In the case G(n) = F the integral I-F,I-n(F)/n is the probability that a record occurs in X-1,..., X-n at index n. (1) obtained lower and upper asymptotic bounds for this case, whereas (2) showed the rate of convergence if d = 2. In this paper we derive the exact rate of convergence of I-F,I-n(G(n)) for d greater than or equal to 2 under some restrictions on the distribution function Gn. Some related results for multivariate Gaussian tails are discussed also.

Keywords

Exact asymptotics, Records, Extreme value distribution, Gaussian sequences, Quadratic programming

Web of science

Create date

03/09/2010 13:06

Last modification date

04/04/2017 16:15