A note on harmonizable and V-bounded processes

Yûichirô Kakihara

Journal of Multivariate Analysis, 1985, vol. 16, issue 1, 140-156

Abstract: Let H be a Hilbert space and B(H) be the algebra of all bounded linear operators on H. Normal Hilbert B(H)-module valued processes are studied over a locally compact abelian group as models for infinite variate or Hilbert space valued stochastic processes. Harmonizability of Rozanov type and V-boundedness are defined for such processes. It is shown that a process is harmonizable if and only if it is V-bounded and continuous. A necessary and sufficient condition is given for a process to have a stationary dilation.

Keywords: normal; Hilbert; B(H)-modules; harmonizable; processes; V-bounded; processes; stationary; dilation; operator; semivariation; orthogonally; scattered; dilation (search for similar items in EconPapers)
Date: 1985
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