Vol. 65, No. 1, 1976

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ISSN: 0030-8730
Level crossing probabilities for a multi-parameter Brownian process

Peggy Strait

Vol. 65 (1976), No. 1, 223–232
Abstract

Let {ξs1,s2 : −∞ < s1,< ,−∞ < s2 < ∞} be a Gaussian process with ξs1,s2 = 0 if s1 = 0 or s2 = 0, mean values E(ξs1,s2) = 0, and covariances E(ξs1,s2ξs1,s1) = 12min(s1,s1)min(s2,s2). This is the two parameter Brownian process studied by J. D. Kuelbs, W. J. Park, P. T. Strait, and J. Yeh. In this paper, upper and lower bounds for level crossing probabilities of this process are derived.

Mathematical Subject Classification 2000
Primary: 60G15
Secondary: 60J65
Milestones
Received: 19 August 1975
Published: 1 July 1976
Authors
Peggy Strait