Bulletin of the
Korean Mathematical Society BKMS

In 1992, the author introduced the definition and the properties of Wiener measure over paths in abstract Wiener space and this measure was investigated extensively by some mathematicians. In 2002, the author and Dr. Im presented an article for analogue of Wiener measure and its applications which is the generalized theory of Wiener measure theory. In this note, we will derive the analogue of Wiener measure over paths in abstract Wiener space and establish two integration formulae, one is similar to the Wiener integration formula and another is similar to simple formula for conditional Wiener integral. Furthermore, we will give some examples for our formulae.

Keywords: analogue of Wiener measure, measure-valued measure, Bartle integral, Bochner integral, stochastically independent, conditional expectation

MSC numbers: Primary 28C20; Secondary 28C35