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

Abstract

In this paper, we define the generalized conditional transform with respect to the Gaussian process. We then establish the integration formulas for the generalized conditional transform with respect to the Gaussian process in terms of the generalized conditional ⋄-product and the first variation. Also, we show that the generalized conditional transform with respect to the Gaussian process for the first variation of F can be expressed in terms of the ordinary function space integral of F multiplied by a linear factor.

Keywords:

• generalized Brownian motion process
• Gaussian process
• generalized conditionaltransform
• generalized conditional ⋄-product
• first variation
• Cameron–Storvick theorem

AMS Subject Classification:

• Primary: 60J25
• 28C20

Acknowledgments

The authors thank the referees for their helpful suggestions which led to the present version of this paper.

Disclosure statement

No potential conflict of interest was reported by the authors.