The rate of convergence of the Hurst index estimate for a stochastic differential equation

Kęstutis Kubilius; Viktor Skorniakov; Kostiantyn Ralchenko

doi:10.15388/NA.2017.2.9

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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