An evaluation of the conditional Yeh-Wiener integral

Kun Soo Chang, Jae Moon Ahn and Joo Sup Chang

Vol. 124 (1986), No. 1, 107–117

DOI: 10.2140/pjm.1986.124.107

Abstract

Yeh obtained the conditional Wiener integral of

given x(t) where x is in Wiener space C[0,t] and V is a function on R¹ satisfying certain conditions. In this paper we extend Yeh’s result to the conditional Yeh-Wiener integral of exp{−∫ ₀^t∫ ₀^sV [x(u,v)]dudv} given x(s,t) where x is in Yeh-Wiener space C₂(Q) and V is a nonnegative continuous function on R¹ satisfying the condition

Mathematical Subject Classification 2000

Primary: 60J65

Secondary: 60G15, 60G60

Milestones

Received: 19 March 1985

Revised: 5 July 1985

Published: 1 September 1986