Skip to main content
padlock icon - secure page this page is secure

Computing the covariance of two Brownian area integrals

Buy Article:

$52.00 + tax (Refund Policy)

We compute the expected product of two correlated Brownian area integrals, a problem that arises in the analysis of a popular sorting algorithm. Along the way we find three different formulas for the expectation of the product of the absolute values of two standard normal random variables with correlation θ. These two formulas are found: (a) via conditioning and the non-central chi-square distribution; (b) via Mehler’s formula; (c) by representing the correlated normal random variables in terms of independent normal’s and integration using polar coordinates.
No References
No Citations
No Supplementary Data
No Article Media
No Metrics

Keywords: Brownian bridge; Mehler’s formula; bivariate normal distribution; correlation; expectation; non-central chi-square; product of absolute values

Document Type: Original Article

Affiliations: 1: University of Washington, U.S.A. [email protected] 2: Department of Statistics, Oregon State University, U.S.A. [email protected]

Publication date: February 1, 2002

  • Access Key
  • Free content
  • Partial Free content
  • New content
  • Open access content
  • Partial Open access content
  • Subscribed content
  • Partial Subscribed content
  • Free trial content
Cookie Policy
X
Cookie Policy
Ingenta Connect website makes use of cookies so as to keep track of data that you have filled in. I am Happy with this Find out more