The Annals of Applied Probability

Pathwise stability of likelihood estimators for diffusions via rough paths

Joscha Diehl, Peter Friz, and Hilmar Mai

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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.

Article information

Source
Ann. Appl. Probab., Volume 26, Number 4 (2016), 2169-2192.

Dates
Received: March 2015
First available in Project Euclid: 1 September 2016

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1472745455

Digital Object Identifier
doi:10.1214/15-AAP1143

Mathematical Reviews number (MathSciNet)
MR3543893

Zentralblatt MATH identifier
06653634

Subjects
Primary: 62M05: Markov processes: estimation 62F99: None of the above, but in this section
Secondary: 60H99: None of the above, but in this section

Keywords
Maximum likelihood estimation robust estimation rough paths analysis

Citation

Diehl, Joscha; Friz, Peter; Mai, Hilmar. Pathwise stability of likelihood estimators for diffusions via rough paths. Ann. Appl. Probab. 26 (2016), no. 4, 2169--2192. doi:10.1214/15-AAP1143. https://projecteuclid.org/euclid.aoap/1472745455


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