Asymptotic Properties of Drift Parameter Estimator Based on Discrete Observations of Stochastic Differential Equation Driven by Fractional Brownian Motion

Yuliya Mishura (), Kostiantyn Ral’chenko (), Oleg Seleznev () and Georgiy Shevchenko ()
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Yuliya Mishura: Taras Shevchenko National University of Kyiv
Kostiantyn Ral’chenko: Taras Shevchenko National University of Kyiv
Oleg Seleznev: University of Umea
Georgiy Shevchenko: Taras Shevchenko National University of Kyiv

A chapter in Modern Stochastics and Applications, 2014, pp 303-318 from Springer

Abstract: Abstract 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.

Keywords: Stochastic Differential Equation; Fractional Derivative; Maximum Likelihood Estimator; Wiener Process; Fractional Brownian Motion (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-319-03512-3_17

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DOI: 10.1007/978-3-319-03512-3_17

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