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Asymptotic properties of drift parameter estimator based on discrete observations of stochastic differential equation driven by fractional brownian motion
Department of Probability Theory, Statistics and Actuarial Mathematics, Taras Shevchenko National University of Kyiv, Ukraine .
Department of Probability Theory, Statistics and Actuarial Mathematics, Taras Shevchenko National University of Kyiv, Ukraine.
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
Department of Probability Theory, Statistics and Actuarial Mathematics, Taras Shevchenko National University of Kyiv, Ukraine .
2014 (English)In: Modern stochastics and applications / [ed] Volodymyr Korolyuk, Nikolaos Limnios, Yuliya Mishura, Lyudmyla Sakhno, Georgiy Shevchenko, Springer, 2014, 303-318 p.Chapter in book (Refereed)
Abstract [en]

In this chapter, we consider a problem of statistical estimation of an unknown drift parameter for a stochastic differential equation driven by fractional Brownian motion. Two estimators based on discrete observations of solution to the stochastic differential equations are constructed. It is proved that the estimators converge almost surely to the parameter value, as the observation interval expands and the distance between observations vanishes. A bound for the rate of convergence is given and numerical simulations are presented. As an auxilliary result of independent interest we establish global estimates for fractional derivative of fractional Brownian motion.

Place, publisher, year, edition, pages
Springer, 2014. 303-318 p.
Series
Springer optimization and its applications, ISSN 1931-6828 ; 90
National Category
Probability Theory and Statistics
Research subject
Mathematical Statistics
Identifiers
URN: urn:nbn:se:umu:diva-81372DOI: 10.1007/978-3-319-03512-3_17ISBN: 978-3-319-03511-6 (print)ISBN: 978-3-319-03512-3 (print)OAI: oai:DiVA.org:umu-81372DiVA: diva2:654775
Available from: 2013-10-08 Created: 2013-10-08 Last updated: 2015-06-01Bibliographically approved

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Asymptotic Properties of Drift Parameter Estimator Based on Discrete Observations of Stochastic Differential Equation Driven by Fractional Brownian Motion(171 kB)179 downloads
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Publisher's full texthttp://arxiv.org/abs/1309.6596

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