Integration with respect to analogue of Wiener measure over paths in abstract Wiener measure
by
Kun Sik Ryu
Han Nam University, Daejeon, South Korea

In 1992, the author introduced the definition of Wiener measure over paths in abstract Wiener space and this measure was investigated extensively by some mathematicians [1,2,4,5]. In 2002, the author and professor Im presented an article for analogue of Wiener measure and its applications [3]. In this note, we will derive the analogue of Wiener measure over paths in abstract Wiener space, find two integration formulae for the measure and negative examples for it.

REFERENCES

[1] K.S.Ryu, The Wiener integral over paths in abstract Wiener space, J. Korean Math. Soc., Vol. 29, No. 2, 1992

[2] K.S.Ryu and S.C.Yoo, The existence theorem and formula for an operator-valued function space integral over paths in abstract Wiener space, Houston J. Math., Vol. 28, No. 3, 2002

[3] K.S.Ryu and M.K.Im, A measure-valued analogue of Wiener measure and the measure-valued Feynman-Kac formula, Trans. Amer. Math. Soc., Vol. 354, No. 12, 2002

[4] I.Yoo, The analytic Feynman integral over paths in abstract Wiener space, Comm. Korean Math. Soc., Vol. 10, 1995

[5] I.Yoo and B.S.Kim, Analytic Feynman integrable functions over paths in abstract Wiener space, Far East J. Math. Sci., Vol. 6, 1998

Date received: June 3, 2008