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August 2016 Pathwise stability of likelihood estimators for diffusions via rough paths
Joscha Diehl, Peter Friz, Hilmar Mai
Ann. Appl. Probab. 26(4): 2169-2192 (August 2016). DOI: 10.1214/15-AAP1143

Abstract

We consider the classical estimation problem of an unknown drift parameter within classes of nondegenerate diffusion processes. Using rough path theory (in the sense of T. Lyons), we analyze the Maximum Likelihood Estimator (MLE) with regard to its pathwise stability properties as well as robustness toward misspecification in volatility and even the very nature of the noise. Two numerical examples demonstrate the practical relevance of our results.

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Joscha Diehl. Peter Friz. Hilmar Mai. "Pathwise stability of likelihood estimators for diffusions via rough paths." Ann. Appl. Probab. 26 (4) 2169 - 2192, August 2016. https://doi.org/10.1214/15-AAP1143

Information

Received: 1 March 2015; Published: August 2016
First available in Project Euclid: 1 September 2016

zbMATH: 06653634
MathSciNet: MR3543893
Digital Object Identifier: 10.1214/15-AAP1143

Subjects:
Primary: 62F99, 62M05
Secondary: 60H99

Rights: Copyright © 2016 Institute of Mathematical Statistics

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Vol.26 • No. 4 • August 2016
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