A note on harmonizable and V-bounded processes

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.