Theory of Probability and Mathematical Statistics
Asymptotic properties of non-standard drift parameter estimators in the models involving fractional Brownian motion
Meriem Bel Hadj Khlifa, Yuliya Mishura, and Mounir Zili
Abstract: We investigate the problem of estimation of the unknown drift parameter in the stochastic differential equations driven by fractional Brownian motion, with the coefficients supplying standard existence–uniqueness demands. We consider a particular case when the ratio of drift and diffusion coefficients is non-random, and establish the asymptotic strong consistency of the estimator with different ratios, from many classes of non-random standard functions. Simulations are provided to illustrate our results, and they demonstrate the fast rate of convergence of the estimator to the true value of a parameter.
Keywords: . Parameter estimators, fractional Brownian motion, strong consistency, estimation of fractional derivatives.
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