A Karhunen-Loeve expansion for a mean-centered Brownian bridge

Paul Deheuvels

Statistics & Probability Letters, 2007, vol. 77, issue 12, 1190-1200

Abstract: The processes of the form , where K is a constant, and B(·) a Brownian bridge, are investigated. We show that and are both Brownian bridges, and establish the independence of and , this implying that the law of coincides with the conditional law of B, given that . We provide the Karhunen-Loeve expansion on [0,1] of , making use of the Bessel functions J1/2 and J3/2. Applications and variants of these results are discussed. In particular, we establish a comparison theorem concerning the supremum distributions of and on [0,1].

Keywords: Gaussian; processes; Karhunen-Loeve; expansions; Wiener; process; Brownian; bridge; Cramer-von; Mises; tests; of; fit; Tests; of; goodness; of; fit (search for similar items in EconPapers)
Date: 2007
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Citations: View citations in EconPapers (1)

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