Some Estimation Problems in Infinite Dimensional Gaussian White Noise

I. Ibragimov and R. Khasminskii
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I. Ibragimov: St.-Petersburg branch of the Steklov Mathematical Institute
R. Khasminskii: Department of Mathematics Wayne State University

Chapter 16 in Festschrift for Lucien Le Cam, 1997, pp 259-274 from Springer

Abstract: Abstract Statistical problems for infinite dimensional Gaussian white noise arise in a natural way when one tries to study statistical questions connected with stochastic partial differential equations (Hübner, Khas’minskii & Rozovskii 1993). In this paper we analyze the simplest situation of estimation of the shift parameter in Gaussian white noise. We considered the one-dimensional case in Ibragimov & Has’minskii (1977). It turns out that the problems for infinite dimensional white noise have a much richer analytical content, as we hope to show in this and other papers that we are planning to write.

Keywords: Consistent Estimator; Stochastic Partial Differential Equation; Observation Scheme; Shannon Capacity; Cylindrical Wiener Process (search for similar items in EconPapers)
Date: 1997
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4612-1880-7_16

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DOI: 10.1007/978-1-4612-1880-7_16

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