Strongly and weakly harmonizable stochastic processes of H-valued random variables. (English) Zbl 0589.60034

Author’s summary: Let H be a Hilbert space and (\(\Omega\),\({\mathcal F},\mu)\) be a probability measure space. Consider the Hilbert space \(L^ 2_ 0(\Omega,H)\) consisting of all H-valued strong random variables on \(\Omega\) with zero mean which are square integrable with respect to \(\mu\). The author studies \(L^ 2_ 0(\Omega;H)\)-valued processes. It is shown that, as in the scalar valued case, every weakly harmonizable process is approximated pointwisely on R by a sequence of strong harmonizable processes. To prove this he obtains a series representation of a continuous process.
Reviewer: H.Salehi


60G12 General second-order stochastic processes
60B11 Probability theory on linear topological spaces
46G10 Vector-valued measures and integration
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