The rate of convergence of estimate for Hurst index of fractional Brownian motion involved into stochastic differential equation

Abstract

We consider stochastic differential equation involving pathwise integral with respect to fractional Brownian motion. The estimates for the Hurst parameter are constructed according to first- and second-order quadratic variations of observed values of the solution. The rate of convergence of these estimates to the true value of a parameter is established.

arXiv comment20 pages

References in corpus (2)

• Asymptotic behavior of weighted quadratic and cubic variations of fractional Brownian motion
• Estimation in models driven by fractional Brownian motion

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