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

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

2011-11-29

arxiv.org/abs/1111.6711v1

Mathematics

Probability

20 pages

Scientific paper

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.

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