Characterization Theorems for Generalized Functionals of Discrete-Time Normal Martingale
Joint Authors
Source
Issue
Vol. 2015, Issue 2015 (31 Dec. 2015), pp.1-6, 6 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2015-04-19
Country of Publication
Egypt
No. of Pages
6
Main Subjects
Abstract EN
We aim at characterizing generalized functionals of discrete-time normal martingales.
Let M = ( M n ) n ∈ N be a discrete-time normal martingale that has the chaotic representation property.
We first construct testing and generalized functionals of M with an appropriate orthonormal basis for M ’s square integrable functionals.
Then we introduce a transform, called the Fock transform, for these functionals and characterize them via the transform.
Several characterization theorems are established.
Finally we give some applications of these characterization theorems.
Our results show that generalized functionals of discrete-time normal martingales can be characterized only by growth condition, which contrasts sharply with the case of some continuous-time processes (e.g., Brownian motion), where both growth condition and analyticity condition are needed to characterize generalized functionals of those continuous-time processes.
American Psychological Association (APA)
Wang, Caishi& Chen, Jinshu. 2015. Characterization Theorems for Generalized Functionals of Discrete-Time Normal Martingale. Journal of Function Spaces،Vol. 2015, no. 2015, pp.1-6.
https://search.emarefa.net/detail/BIM-1068311
Modern Language Association (MLA)
Wang, Caishi& Chen, Jinshu. Characterization Theorems for Generalized Functionals of Discrete-Time Normal Martingale. Journal of Function Spaces No. 2015 (2015), pp.1-6.
https://search.emarefa.net/detail/BIM-1068311
American Medical Association (AMA)
Wang, Caishi& Chen, Jinshu. Characterization Theorems for Generalized Functionals of Discrete-Time Normal Martingale. Journal of Function Spaces. 2015. Vol. 2015, no. 2015, pp.1-6.
https://search.emarefa.net/detail/BIM-1068311
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1068311