On estimation of time dependent spatial signal in Gaussian white noise

P. L. Chow*, R. Khasminskii, R. Liptser

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

We consider an estimation problem for time dependent spatial signal observed in a presence of additive cylindrical Gaussian white noise of a small intensity ε. Under known a priori smoothness of the signal estimators with asymptotically the best in the mimimax sense risk convergence rate in ε to zero are proposed. Moreover, on-line estimators for the signal and its derivatives in t are also created.

Original languageEnglish
Pages (from-to)161-175
Number of pages15
JournalStochastic Processes and their Applications
Volume96
Issue number1
DOIs
StatePublished - Nov 2001

Funding

FundersFunder number
National Science FoundationDMS 9971608
Directorate for Mathematical and Physical Sciences9971608

    Keywords

    • Gaussian random measure
    • Kernel estimator
    • On-line estimator
    • Projection estimator

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