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Teoriya Veroyatnostei i ee Primeneniya, 2001, Volume 46, Issue 1, Pages 164–169
DOI: https://doi.org/10.4213/tvp4034 (Mi tvp4034) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Short Communications

On L2 Efficiency of an Empiric Distribution for Ergodic Diffusion Processes

Yu. A. Kutoyantsa, I. Negrib

a Université du Maine
b University of Bergamo
Full-text PDF (690 kB) Citations (3)
DOI: https://doi.org/10.4213/tvp4034
Abstract: The problem of the estimation of a stationary distribution function of an ergodic diffusion process with unknown trend coefficient is considered. An elementary proof of the lower minimax bound with integrated mean square error is proposed and it is shown that the empiric distribution attains this bound.
Keywords: ergodic diffusion process, lower bound, nonparametric estimation, asymptotic efficiency.
Received: 27.10.1998
English version:
Theory of Probability and its Applications, 2002, Volume 46, Issue 1, Pages 140–146
DOI: https://doi.org/10.1137/S0040585X97978816
Bibliographic databases:
Document Type: Article
Language: English
Citation: Yu. A. Kutoyants, I. Negri, “On L2 Efficiency of an Empiric Distribution for Ergodic Diffusion Processes”, Teor. Veroyatnost. i Primenen., 46:1 (2001), 164–169; Theory Probab. Appl., 46:1 (2002), 140–146
Citation in format AMSBIB
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\paper On $L_2$ Efficiency of an Empiric Distribution for Ergodic Diffusion Processes
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\pages 164--169
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\zmath{https://zbmath.org/?q=an:0990.62073}
\transl
\jour Theory Probab. Appl.
\yr 2002
\vol 46
\issue 1
\pages 140--146
\crossref{https://doi.org/10.1137/S0040585X97978816}
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Linking options:
  • https://www.mathnet.ru/eng/tvp4034
  • https://doi.org/10.4213/tvp4034
  • https://www.mathnet.ru/eng/tvp/v46/i1/p164
    • This publication is cited in the following 3 articles:
    1. Sören Christensen, Claudia Strauch, “Nonparametric learning for impulse control problems—Exploration vs. exploitation”, Ann. Appl. Probab., 33:2 (2023)  crossref
    2. Negri I., “Efficiency of a Class of Unbiased Estimators for the Invariant Distribution Function of a Diffusion Process”, Communications in Statistics–Theory and Methods, 39:1 (2010), 177–185  crossref  mathscinet  zmath  isi  scopus
    3. van der Vaart A., van Zanten H., “Donsker theorems for diffusions: Necessary and sufficient conditions”, Annals of Probability, 33:4 (2005), 1422–1451  crossref  mathscinet  zmath  isi  scopus
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теория вероятностей и ее применения Theory of Probability and its Applications
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