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Some Estimation Problems in Infinite Dimensional Gaussian White Noise

In: Festschrift for Lucien Le Cam

Author

Listed:
  • I. Ibragimov

    (St.-Petersburg branch of the Steklov Mathematical Institute)

  • R. Khasminskii

    (Department of Mathematics Wayne State University)

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.

Suggested Citation

  • I. Ibragimov & R. Khasminskii, 1997. "Some Estimation Problems in Infinite Dimensional Gaussian White Noise," Springer Books, in: David Pollard & Erik Torgersen & Grace L. Yang (ed.), Festschrift for Lucien Le Cam, chapter 16, pages 259-274, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-1880-7_16
    DOI: 10.1007/978-1-4612-1880-7_16
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