Hostname: page-component-cd9895bd7-p9bg8 Total loading time: 0 Render date: 2024-12-29T06:17:39.252Z Has data issue: false hasContentIssue false

Multivariate normal integrals for highly correlated samples from a wiener process

Published online by Cambridge University Press:  14 July 2016

James L. Lewis
Affiliation:
Purdue University

Extract

If X1, …, Xn obey a multivariate normal distribution with zero means, then the probability that Xi > a for all i = 1, …, n is often called a multivariate normal integral. Such integrals have been considered by various investigators, particularly when a = 0. (For a bibliography, see Gupta.)

Type
Research Papers
Copyright
Copyright © Sheffield: Applied Probability Trust 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Gupta, S. S. (1963) Probability integrals of multivariate normal and multivariate t. Bibliography on the multivariate normal integrals and related topics. Ann. Math. Statist. 34, 792828, 829838.CrossRefGoogle Scholar
[2] Parzen, E. (1962) Stochastic Processes. Holden-Day, San Francisco.Google Scholar
[3] Spitzer, F. (1956) A combinatorial lemma and its application to probability theory. Trans. Amer. Math. Soc. 82, 323339.Google Scholar
[4] Anis, A. A. and Lloyd, E. H. (1953) On the range of partial sums of a finite number of independent normal variates. Biometrika 40, 3542.CrossRefGoogle Scholar
[5] U. S. DEPT, OF COMMERCE, NATIONAL BUREAU OF STANDARDS (1959). Tables of the Bivariate Normal Integral and Related Functions. Applied Mathematics Series 50. U. S. Government Printing Office, Washington.Google Scholar
[6] Rice, S. O. (1958) Distribution of the duration of fades in radio transmission. Bell Syst. Tech. J. 37, 581635.CrossRefGoogle Scholar
[7] Itô, K. and Mckean, H. P. Jr. (1965) Diffusion Processes and their Sample Paths. Academic Press, New York.Google Scholar
[8] McFadden, J. A. (1967) On a class of Gaussian processes for which the mean rate of crossings is infinite. J. R. Statist. Soc. B 29, No. 3.Google Scholar