Accession Number:

ADA207253

Title:

On the Distribution of the Integrated Square of the Ornstein-Uhlenbeck Process

Descriptive Note:

Technical rept.

Corporate Author:

NORTH CAROLINA UNIV AT CHAPEL HILL DEPT OF STATISTICS

Personal Author(s):

Report Date:

1988-01-01

Pagination or Media Count:

25.0

Abstract:

Using functional integral methods, one calculates the Laplace transform of the square of the Ornstein-Uhlenbeck process Xt integrated over 0 or t or T, invert this transform via infinite series, and study the asymptotic behavior as T approaches infinity of the density and distribution functions, as well as these functions conditioned on the event XT 0. We find that the approximation by an inverse Gaussian distribution, introduced earlier by Grenander, Pollak, and Slepian, is asymptotically correct to within a constant factor in the conditional case, but in the unconditional case.

Subject Categories:

  • Numerical Mathematics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE