On complex operator-valued O-U processes, T-positivity, and innovations of Okabe and Masani

This paper gives innovation of an infinite-dimensional isometric Markov stationary process. In terms of this innovation the process is expressed as an Ornstein-Uhlenbeck process. The result includes the innovation results provided earlier by Masani and Okabe. We use techniques of Nagy dilation theor...

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Bibliographic Details
Published inJournal of multivariate analysis Vol. 29; no. 1; pp. 68 - 83
Main Authors Makagon, A, Mandrekar, V
Format Journal Article
LanguageEnglish
Published San Diego, CA Elsevier Inc 01.04.1989
Elsevier
SeriesJournal of Multivariate Analysis
Subjects
Exact sciences and technology
innovation
Mathematics
Probability and statistics
Probability theory and stochastic processes
Sciences and techniques of general use
stationary Markov process
stationary Markov process innovation T-positivity
Stochastic processes
T-positivity
innovation
stationary Markov process
47A20
T-positivity
60G10
Markov process
Innovation
Dilatation
Stationary process
Semigroup
Ornstein Uhlenbeck process
Infinite dimension
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Summary:This paper gives innovation of an infinite-dimensional isometric Markov stationary process. In terms of this innovation the process is expressed as an Ornstein-Uhlenbeck process. The result includes the innovation results provided earlier by Masani and Okabe. We use techniques of Nagy dilation theory which also yield a direct proof of the main result of Okabe on the structure of T-positive processes.
ISSN:0047-259X
1095-7243
DOI:10.1016/0047-259X(89)90077-8