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Theory of Probability and Mathematical Statistics

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The local asymptotic normality of a family of measures generated by solutions of stochastic differential equations with a small fractional Brownian motion


Author: T. Androshchuk
Translated by: V. V. Semenov
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 71 (2004).
Journal: Theor. Probability and Math. Statist. 71 (2005), 1-15
MSC (2000): Primary 62F12; Secondary 60G15, 60H10
Published electronically: December 30, 2005
MathSciNet review: 2144316
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Abstract | References | Similar Articles | Additional Information

Abstract: A formula for the likelihood ratio of measures generated by solutions of a stochastic differential equation with a fractional Brownian motion is established in the paper. We find sufficient conditions that the family of measures generated by solutions of such an equation is locally asymptotically normal.


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Additional Information

T. Androshchuk
Affiliation: Department of Probability Theory and Mathematical Statistics, Faculty for Mechanics and Mathematics, National Taras Shevchenko University, Academician Glushkov Avenue, 6, Kyiv 03127, Ukraine
Email: nutaras@univ.kiev.ua

DOI: https://doi.org/10.1090/S0094-9000-05-00643-5
Keywords: Fractional brownian motion, local asymptotic normality of a system of measures, dynamic systems with small noise
Received by editor(s): March 12, 2004
Published electronically: December 30, 2005
Article copyright: © Copyright 2005 American Mathematical Society