UCL logo

UCL Discovery

UCL home » Library Services » Electronic resources » UCL Discovery

Doubly stochastic Hilbertian processes

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

Full text not available from this repository.

Abstract

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
UCL classification:UCL > School of BEAMS > Faculty of Maths and Physical Sciences > Statistical Science

Archive Staff Only: edit this record