Vol. 53, No. 2, 1974

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Probabilities of Wiener paths crossing differentiable curves

Chull Park and S. R. Paranjape

Vol. 53 (1974), No. 2, 579–583
Abstract

Let {W(t);t 0} be the standard Wiener process. The probabilities P[sup0tTW(t) b] and P[sup0tTW(t) at b] are well known. This paper gives the probabilities of the type P[sup0tTW(t) f(t) b] for a large class of differentiable functions f(t) by the use of integral equation techniques.

Mathematical Subject Classification 2000
Primary: 60J65
Milestones
Received: 12 April 1973
Revised: 20 January 1974
Published: 1 August 1974
Authors
Chull Park
S. R. Paranjape