PROBABILITIES OF ANALOGUE OF WIENER PATHS CROSSING CONTINUOUSLY DIFFERENTIABLE CURVES

Abstract

Let ϕ be a complete probability measure on R, let mϕ be the analogue of Wiener measure over paths on [0, T ] and let f (t) be continuously differentiable on [0, T ]. In this note, we give the analogue of Wiener measure mϕ of {x in C[0, T ]|x(0) < f (0) and x(s0) ≥ f (s0) for some s0 in [0, T ]} by use of integral equation techniques. This result is a generalization of Park and Paranjape's 1974 result[1].

This article was migrated from the previous system via automation. The abstract may not be written correctly. Please view the PDF file.