Parameter Estimation for α-Fractional Bridges

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

Covariance 

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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