Hurst index estimation in stochastic differential equations driven by fractional Brownian motion
Probability
2019-03-07 v1 Statistics Theory
Statistics Theory
Abstract
We consider the problem of Hurst index estimation for solutions of stochastic differential equations driven by an additive fractional Brownian motion. Using techniques of the Malliavin calculus, we analyze the asymptotic behavior of the quadratic variations of the solution, defined via higher order increments. Then we apply our results to construct and study estimators for the Hurst index.
Cite
@article{arxiv.1903.02364,
title = {Hurst index estimation in stochastic differential equations driven by fractional Brownian motion},
author = {Jan Gairing and Peter Imkeller and Radomyra Shevchenko and Ciprian A. Tudor},
journal= {arXiv preprint arXiv:1903.02364},
year = {2019}
}