The rate of convergence of the Hurst index estimate for a stochastic differential equation
Articles
Kęstutis Kubilius
Vilnius University
Viktor Skorniakov
Vilnius University
Kostiantyn Ralchenko
Taras Shevchenko National University of Kyiv, Ukraine
Published 2017-03-15
https://doi.org/10.15388/NA.2017.2.9
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Keywords

fractional Brownian motion
stochastic differential equation
second-order quadratic variations
estimates of Hurst parameter
rate of convergence

How to Cite

Kubilius K., Skorniakov V. and Ralchenko K. (2017) “The rate of convergence of the Hurst index estimate for a stochastic differential equation”, Nonlinear Analysis: Modelling and Control, 22(2), pp. 273-284. doi: 10.15388/NA.2017.2.9.

Abstract

We consider an estimator of the Hurst parameter of stochastic differential equation with respect to a fractional Brownian motion and establish the rate of convergence of this estimator to the true value of H when the diameter of partition of observation interval tends to zero.

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