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Publication Date:
August 2009
ISSN:
1569-397X
DOI:
10.1515/ROSE.2009.012

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Random Operators and Stochastic Equations

Editor-in-Chief: Girko, Vyacheslav

Managing Editor: Molchanov, S.

Editorial Board Member: Accardi, L. / Albeverio, Sergio / Carmona, R. / Casati, G. / Christopeit, N. / Domanski, C. / Drygas, Hilmar / Gupta, A.K. / Ibragimov, I. / Kirsch, Werner / Klein, A. / Kondratyev, Yuri / Kurotschka, V. / Leonenko, N. / Loubaton, Philippe / Orsingher, E. / Pastur, L. / Rodrigues, Waldyr A. / Shiryaev, Albert / Turbin, A.F. / Veretennikov, Alexandre

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On one property of the Wiener integral and its statistical application

Petre Babilua1 / Elizbar Nadaraya2 / Albert Shatashvili3 / Grigol Sokhadze4

1Faculty of Exact and Natural Sciences, Iv. Javakhishvili Tbilisi State University 2, University St., Tbilisi 0143, Georgia. Email: p_babilua@yahoo.com

2Faculty of Exact and Natural Sciences, Iv. Javakhishvili Tbilisi State University, 2, University St., Tbilisi 0143, Georgia. Email: elizbar.nadaraya@tsu.ge

3Institute of Applied Mathematics and Mechanics, R. Luxemburg str. 74, Donetsk 83055, Ukraine. Email: shatal@bk.ru

4A. Tsereteli State University 59, Tamar Mepe St., Kutaisi 4600, Georgia. Email: giasokhi1@i.ua

Citation Information: Random Operators and Stochastic Equations. Volume 17, Issue 2, Pages 173–187, ISSN (Online) 1569-397x, ISSN (Print) 0926-6364, DOI: 10.1515/ROSE.2009.012, August 2009

Publication History:
Received:
2009-01-12
Published Online:
2009-08-19

Abstract

For the Wiener integral, one property of inversion is established. This property is used for the construction of nonparametric statistical estimation of the unknown logarithmic derivative for the distribution of random processes, which is observed in Wiener noise.

Key words.: Wiener integral; logarithmic derivative; nonparametric estimator

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