The moments of the area under reflected Brownian bridge conditional on its local time at zero. (2000)

• Record Type: Journal Article
• Authors: Knight, Frank B.
• Is Part Of: Journal of applied mathematics and stochastic analysis. Volume 13:Number 2(2000)
• Page Start: 99
• Page End: 124
• Publication Date: 2000
• Subjects: Brownian bridge -- local time -- Pitman process -- method of M. Kac -- Hermite equations; Mathematical models -- Periodicals; Computer simulation -- Periodicals; Computer science -- Mathematics -- Periodicals; Computer science -- Mathematics; Computer simulation; Mathematical models; Applied Mathematics; Periodicals; Electronic journals; 519.22
• DOI: 10.1155/S1048953300000137
• Languages: English
• ISSNs: 1048-9533

Abstract

Abstract : This paper develops a recursion formula for the conditional moments of the area under the absolute value of Brownian bridge given the local time at 0. The method of power series leads to a Hermite equation for the generating function of the coefficients which is solved in terms of the parabolic cylinder functions. By integrating out the local time variable, this leads to an integral expression for the joint moments of the areas under the positive and negative parts of the Brownian bridge.