A characterization of operators on functionals of discrete-time normal martingales. Issue 2 (4th March 2017)

• Record Type: Journal Article
• Authors: Wang, Caishi; Chen, Jinshu
• Is Part Of: Stochastic analysis and applications. Volume 35:Issue 2(2017)
• Page Start: 305
• Page End: 316
• Publication Date: 2017-03-04
• Subjects: Discrete-time normal martingale -- Gel'fand triple -- operator -- Fock transform -- characterization theorem; Primary: 60H40 -- Secondary: 47B38; Stochastic analysis -- Periodicals; 519.2205
• DOI: 10.1080/07362994.2016.1248779
• Languages: English
• ISSNs: 0736-2994

Abstract

ABSTRACT: In this article, we aim at characterizing operators acting on functionals of discrete-time normal martingales. Let be a discrete-time normal martingale that has the chaotic representation property. We first introduce a transform, called 2D-Fock transform, for operators from the testing functional space to the generalized functional space of M . Then we characterize continuous linear operators from to via their 2D-Fock transforms. Our characterization theorems show that there exists a one-to-one correspondence between continuous linear operators from to and functions on Γ × Γ that only satisfy some type of growth condition, where Γ designates the finite power set of . Finally, we give some applications of our characterization theorems.