Vol. 94, No. 2, 1981

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ISSN: 0030-8730
Representations of Gaussian processes by Wiener processes

Chull Park

Vol. 94 (1981), No. 2, 407–415
Abstract

Let {X(t),a t b} and {W(t),0 t < ∞} be a Gaussian process and the standard Wiener process, respectively. Investigating covariance structure of X(t), the paper gives various representations of X(t) in terms of W(t), including stochastic integral representations. Some of these representations are useful in finding hitherto unknown barrier-crossing probabilities of X(t).

Mathematical Subject Classification 2000
Primary: 60G15
Secondary: 60J65
Milestones
Received: 18 February 1980
Published: 1 June 1981
Authors
Chull Park