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A note on the cross-covariance operator and on congruence relations for Hilbert space valued stochastic processes

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  • King, David

Abstract

Explicit formulas are derived for the congruence mappings that connect three Hilbert spaces associated with a second-order stochastic process. In particular, an insightful expression is obtained for the mapping that connects a process to its corresponding reproducing kernel Hilbert space. In addition, a useful infinite dimensional extension of a result from Khatri (1976) which pertains to cross-covariance operators is provided.

Suggested Citation

  • King, David, 2010. "A note on the cross-covariance operator and on congruence relations for Hilbert space valued stochastic processes," Statistics & Probability Letters, Elsevier, vol. 80(5-6), pages 361-365, March.
    • Handle: RePEc:eee:stapro:v:80:y:2010:i:5-6:p:361-365
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    References listed on IDEAS

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    1. C. Khatri, 1976. "A note on multiple and canonical correlation for a singular covariance matrix," Psychometrika, Springer;The Psychometric Society, vol. 41(4), pages 465-470, December.
    2. Eubank, R.L. & Hsing, Tailen, 2008. "Canonical correlation for stochastic processes," Stochastic Processes and their Applications, Elsevier, vol. 118(9), pages 1634-1661, September.
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