An evaluation formula for the Wiener integrals via the bounded linear operator

Abstract

When we evaluate the Wiener integral involving the stochastic inner product via a bounded linear operator, there are some problems to calculate the Wiener integral as seen Section 2 below.
In this paper, we give an idea to calculate the Wiener integral involving the stochastic inner product via a bounded linear operator. We then establish a theorem regarding this process. Our research result is a form of solving a problem that could not be solved before. Therefore, the previous research results corollaries of our research results.