Hurst Index Estimation in Stochastic Differential Equations Driven by Fractional Brownian Motion

Jan Gairing, Peter Imkeller, Radomyra Shevchenko and Ciprian Tudor ()
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Jan Gairing: Ludwig-Maximilians-Universität München
Peter Imkeller: Humboldt-Universität zu Berlin
Radomyra Shevchenko: Technische Universität Dortmund
Ciprian Tudor: CNRS, Université de Lille 1

Journal of Theoretical Probability, 2020, vol. 33, issue 3, 1691-1714

Abstract: 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.

Keywords: Hurst index estimation; Stochastic differential equation; Fractional Brownian motion; Quadratic variation; Malliavin calculus; Central limit theorem; 60G15; 60H05; 60G18 (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (5)

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DOI: 10.1007/s10959-019-00925-w

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