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# Theory of Probability and Mathematical Statistics (Teoriya Imovirnostei ta Matematychna Statystyka)

## The Wold decomposition of Hilbertian periodically correlated processes

### A. Zamani, Z. Sajjadnia, M. Hashemi

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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