SCALE TRANSFORMATIONS FOR PRESENT POSITION-INDEPENDENT CONDITIONAL EXPECTATIONS

- Journal title : Journal of the Korean Mathematical Society
- Volume 53, Issue 3, 2016, pp.709-723
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/JKMS.j150285

Title & Authors

SCALE TRANSFORMATIONS FOR PRESENT POSITION-INDEPENDENT CONDITIONAL EXPECTATIONS

Cho, Dong Hyun;

Cho, Dong Hyun;

Abstract

Let C[0, t] denote a generalized Wiener space, the space of real-valued continuous functions on the interval [0, t] and define a random vector by , where 0 < < < < t is a partition of [0, t] and with a.e. In this paper we will introduce a simple formula for a generalized conditional Wiener integral on C[0, t] with the conditioning function and then evaluate the generalized analytic conditional Wiener and Feynman integrals of the cylinder function for , where and e is a unit element in . Finally we express the generalized analytic conditional Feynman integral of F as two kinds of limits of non-conditional generalized Wiener integrals of polygonal functions and of cylinder functions using a change of scale transformation for which a normal density is the kernel. The choice of a complete orthonormal subset of used in the transformation is independent of e and the conditioning function does not contain the present positions of the generalized Wiener paths.

Keywords

analytic conditional Feynman integral;analytic conditional Wiener integral;conditional Wiener integral;Wiener integral;Wiener space;

Language

English

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