Conditional Transform With Respect to the Gaussian Process Involving the Conditional Convolution Product and the First Variation

Abstract

Abstract. In this paper, we define a conditional transform with respect to the Gaussian process, the conditional convolution product and the first variation of functionals via the Gaussian process. We then examine various relationships of the conditional transform with respect to the Gaussian process, the conditional convolution product and the first variation for functionals F in Sα [5,8].

A new expression for the transform with respect to the Gaussian process

“…In this section we first state several definitions and then we introduce various notations which are used throughout this paper [7,8,10].…”

“…Now, we state the definitions of the transform with respect to the Gaussian process and the first variation, [8,10,11]. Definition 2.1.…”

Generalized conditional transform with respect to the Gaussian process on function space

“…[9,10] Many results for the convolution product are corollaries of the results for the -product. In [8,10], the authors introduced the concept of the conditional transform with respect to the Gaussian process on Wiener space. From this, they obtained various integration formulas involving the conditional -product and the first variation.…”

“…Recently, in [8][9][10], the authors defined a generalized integral transform, based on a Gaussian process. They also presented a modified convolution product, which was different from the definitions given by Equations (1.3) and (1.4).…”