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Doubly stochastic Hilbertian processes

Guillas, S; (2002) Doubly stochastic Hilbertian processes. J APPL PROBAB , 39 (3) 566 - 580.

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In this paper, we consider a Hilbert-space-valued autoregressive stochastic sequence (X-n) with several regimes. We suppose that the underlying process (I-n) which drives the evolution of (X-n) is stationary. Under some dependence assumptions on (I-n), we prove the existence of a unique stationary solution, and with a symmetric compact autocorrelation operator, we can state a law of large numbers with rates and the consistency of the covariance estimator. An overall hypothesis states that the regimes where the autocorrelation operator's norm is greater than 1 should be rarely visited.

Type: Article
Title: Doubly stochastic Hilbertian processes
Keywords: Hilbert, nonlinear, autoregressive, stability, EQUATION, STATIONARITY, COEFFICIENTS
URI: http://discovery.ucl.ac.uk/id/eprint/5399
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