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2015 Drift estimation with non-gaussian noise using Malliavin Calculus
Christian Krein
Electron. J. Statist. 9(2): 2976-3045 (2015). DOI: 10.1214/15-EJS1101

Abstract

The aim of this paper is to show the existence of drift estimators dominating the standard one in continuous-time models of the form $X_{t}=u_{t}+Z_{t}$, where $u_{t}$ is the drift and $Z_{t}$ is either a Brownian martingale or a non-martingale noise living in the second Wiener chaos. Our results are based on the use of Malliavin calculus techniques, and extend previous findings of Privault and Réveillac (2008).

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Christian Krein. "Drift estimation with non-gaussian noise using Malliavin Calculus." Electron. J. Statist. 9 (2) 2976 - 3045, 2015. https://doi.org/10.1214/15-EJS1101

Information

Received: 1 May 2015; Published: 2015
First available in Project Euclid: 5 January 2016

zbMATH: 1335.60124
MathSciNet: MR3439191
Digital Object Identifier: 10.1214/15-EJS1101

Subjects:
Primary: 60H07 , 62M09 , 62M20

Keywords: Cramer-Rao bound , drift estimator , Malliavin calculus , Rosenblatt process , Stein estimator

Rights: Copyright © 2015 The Institute of Mathematical Statistics and the Bernoulli Society

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Vol.9 • No. 2 • 2015
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