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

Authors

  • 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

DOI:

https://doi.org/10.17713/ajs.v43i3.33

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. 

Downloads

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

Issue

Vol. 43 No. 3 (2014)

Section

Articles

License

The Austrian Journal of Statistics publish open access articles under the terms of the Creative Commons Attribution (CC BY) License. 

The Creative Commons Attribution License (CC-BY) allows users to copy, distribute and transmit an article, adapt the article and make commercial use of the article. The CC BY license permits commercial and non-commercial re-use of an open access article, as long as the author is properly attributed.

Copyright on any research article published by the Austrian Journal of Statistics is retained by the author(s). Authors grant the Austrian Journal of Statistics a license to publish the article and identify itself as the original publisher. Authors also grant any third party the right to use the article freely as long as its original authors, citation details and publisher are identified.

 

Manuscripts should be unpublished and not be under consideration for publication elsewhere. By submitting an article, the author(s) certify that the article is their original work, that they have the right to submit the article for publication, and that they can grant the above license.