Work

Clark-Ocone Formula for Generalized Functionals of Discrete-Time Normal Noises

Year: 2018

Type: article

Abstract: The Clark-Ocone formula in the theory of discrete-time chaotic calculus holds only for square integrable functionals of discrete-time normal noises. In this paper, we aim at extending this formula to generalized functionals of discrete-time normal noises. Let Z be a discrete-time normal noise that has the chaotic representation property. We first prove a result concerning the regularity of generalized functionals of Z . Then, we use the Fock transform to define some fundamental operators on generalized functionals of Z and apply the abovementioned regularity result to prove the continuity of these operators. Finally, we establish the Clark-Ocone formula for generalized functionals of Z and show its application results, which include the covariant identity result and the variant upper bound result for generalized functionals of Z .

Source: Journal of Function Spaces

DOI: 10.1155/2018/2954695

Authors: Caishi Wang, Shuai Lin, Ailing Huang

Institution: Northwest Normal University

Language: English

Topic: Stochastic processes and financial applications

Subfield: Finance

Field: Economics, Econometrics and Finance

Domain: Social Sciences

Open Access status: gold

Estimated APC paid: $2,830

Funder: National Natural Science Foundation of China