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

K. Kubilius and Y. Mishura

Stochastic Processes and their Applications, 2012, vol. 122, issue 11, 3718-3739

Abstract: We consider a stochastic differential equation involving a 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 when the diameter of interval partition tends to zero.

Keywords: Fractional Brownian motion; Stochastic differential equation; First- and second-order quadratic variations; Estimates of Hurst parameter; Rate of convergence (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (4)

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DOI: 10.1016/j.spa.2012.06.011

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