A lower bound for boundary crossing probabilities of Brownian bridge/motion with trend

Wolfgang Bischoff and Enkelejd Hashorva

Statistics & Probability Letters, 2005, vol. 74, issue 3, 265-271

Abstract: We show a lower bound for the boundary crossing probability P{[there exists]z[set membership, variant][0,1]:h(z)+B0(z)>u(z)} with B0 a Brownian bridge, h a trend function and u a boundary function. By that we get also a lower bound for the boundary crossing probability P{[there exists]z[set membership, variant][0,1]:h(z)+B0(z) [infinity]. The usual tools to obtain boundary crossing probabilities are finite dimensional approximations of the above probability. In this paper, however, we use the Cameron-Martin-Girsanov formula to obtain a bound of the above probability.

Keywords: Boundary; crossing; probability; Brownian; bridge; with; trend; Brownian; motion; with; trend; Signal-plus-noise; model; Cameron-Martin-Girsanov; formula (search for similar items in EconPapers)
Date: 2005
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Citations: View citations in EconPapers (4)

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