Stochastic Processes and Spectral Analysis for Hilbert C*-Module-Valued Maps
- Authors
- Heo, Jaeseong
- Issue Date
- Jan-2018
- Publisher
- SPRINGERNATURE
- Keywords
- Hilbert C*-module-valued random variable; Covariance operator and correlation operator on a Hilbert C*-module-; C*-algebra-valued bimeasure; Harmonizable stochastic process; Spectral distribution
- Citation
- BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, v.41, no.1, pp.191 - 206
- Indexed
- SCIE
SCOPUS
- Journal Title
- BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY
- Volume
- 41
- Number
- 1
- Start Page
- 191
- End Page
- 206
- URI
- https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/150712
- DOI
- 10.1007/s40840-015-0270-6
- ISSN
- 0126-6705
- Abstract
- In this paper, we consider Hilbert -module-valued random variables and discuss about their expectations, covariance operators and correlation operators by introducing some adjointable operators on Hilbert -modules. We also study Hilbert -module-valued stochastic processes instead of Hilbert space-valued processes as a generalization. Using the characterization of -algebra-valued bimeasures, we prove the equivalence between V-boundedness and harmonizability of Hilbert -module-valued stochastic processes. Finally, we consider Hilbert -module operator-valued stochastic processes and construct spectral distributions associated with Hilbert -module operator-valued stationary stochastic processes.
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