On Drift Parameter Estimation in Models with Fractional Brownian Motion by Discrete Observations

  • Yuliya Mishura Department of Probability Theory, Statistics and Actuarial Mathematics Taras Shevchenko National University of Kyiv
  • Kostiantyn Ralchenko Department of Probability Theory, Statistics and Actuarial Mathematics Taras Shevchenko National University of Kyiv

Abstract

We study a problem of an unknown drift parameter estimation in a stochastic differen- tial equation driven by fractional Brownian motion. We represent the likelihood ratio as a function of the observable process. The form of this representation is in general rather complicated. However, in the simplest case it can be simplified and we can discretize it to establish the a. s. convergence of the discretized version of maximum likelihood estimator to the true value of parameter. We also investigate a non-standard estimator of the drift parameter showing further its strong consistency. 

Published
2014-06-12
How to Cite
Mishura, Y., & Ralchenko, K. (2014). On Drift Parameter Estimation in Models with Fractional Brownian Motion by Discrete Observations. Austrian Journal of Statistics, 43(3), 218-228. https://doi.org/10.17713/ajs.v43i3.33
Section
Articles