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Parameter Estimation for α-Fractional Bridges

  • Khalifa Es-Sebaiy
  • Ivan NourdinEmail author
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 34)

Abstract

Let α, T > 0. We study the asymptotic properties of a least squares estimator for the parameter α of a fractional bridge defined as \(\mathrm{d}X_{t} = -\alpha \, \frac{X_{t}} {T-t}\,\mathrm{d}t + \mathrm{d}B_{t}\), 0 ≤ t < T, where B is a fractional Brownian motion of Hurst parameter \(H > \frac{1} {2}\). Depending on the value of α, we prove that we may have strong consistency or not as t → T. When we have consistency, we obtain the rate of this convergence as well. Also, we compare our results to the (known) case where B is replaced by a standard Brownian motion W.

Keywords

Brownian Motion Fractional Brownian Motion Standard Brownian Motion Strong Consistency Hurst Parameter 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgments

We thank an anonymous referee for his/her careful reading of the manuscript and for his/her valuable suggestions and remarks. Ivan Nourdin was supported in part by the (French) ANR grant ‘Exploration des Chemins Rugueux’

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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Institut de Mathématiques de BourgogneUniversité de BourgogneDijonFrance

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