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Stochastic Processes and Spectral Analysis for Hilbert C*-Module-Valued Maps

Title
Stochastic Processes and Spectral Analysis for Hilbert C*-Module-Valued Maps
Author
허재성
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
Issue Date
2018-01
Publisher
SPRINGER
Citation
BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY, v. 41, no. 1, page. 191-206
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.
URI
https://link.springer.com/article/10.1007%2Fs40840-015-0270-6https://repository.hanyang.ac.kr/handle/20.500.11754/117096
ISSN
0126-6705; 2180-4206
DOI
10.1007/s40840-015-0270-6
Appears in Collections:
COLLEGE OF NATURAL SCIENCES[S](자연과학대학) > MATHEMATICS(수학과) > Articles
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