Distribution estimates of barrier-crossing probabilities of the Yeh-Wiener process

Chull Park and David Lee Skoug

Vol. 78 (1978), No. 2, 455–466

DOI: 10.2140/pjm.1978.78.455

Abstract

Let Q = [0,S] × [0,T] be a rectangle and {X(s,t);s,t ≧ 0} be the two-parameter Yeh-Wiener process. This paper finds probabilities of X(s,t) crossing barriers of the type ast + bs + ct + d on the boundary ∂Q. These probabilities give lower bounds for the yet unknown probabilities of X(s,t) crossing ast + bs + ct + d on Q. The paper also discusses sharper bounds for the latter probabilities.

Mathematical Subject Classification 2000

Primary: 60J65

Secondary: 60G15

Milestones

Received: 30 October 1977

Revised: 9 March 1978

Published: 1 October 1978