Theory of Probability and Mathematical Statistics
The Wold decomposition of Hilbertian periodically correlated processes
A. Zamani, Z. Sajjadnia, M. Hashemi
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Abstract: l{L}}$-Closed Subspaces, Moving Average Representation,
Keywords: $H$-Valued Random Variables,
Bibliography: Correlated Processes, Wold Decomposition.
Abstract: The Wold decomposition of stationary processes is widely applied in
time series prediction and provides interesting
insights into the structure of stationary stochastic processes. In
1971, Kallianpur and Mandrekar, using the notion of resolution of
identity and unitary operators, presented the Wold decomposition
for weakly stationary stochastic processes with values in infinite
dimensional separable Hilbert spaces. This paper aims to
expand the idea of Wold decomposition to Hilbertian periodically
correlated processes, applying the concept of ${\mathcal{L}}$-closed
subspaces.
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