Electronic Journal of Statistics

A general drift estimation procedure for stochastic differential equations with additive fractional noise

Fabien Panloup, Samy Tindel, and Maylis Varvenne

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Abstract

In this paper we consider the drift estimation problem for a general differential equation driven by an additive multidimensional fractional Brownian motion, under ergodic assumptions on the drift coefficient. Our estimation procedure is based on the identification of the invariant measure, and we provide consistency results as well as some information about the convergence rate. We also give some examples of coefficients for which the identifiability assumption for the invariant measure is satisfied.

Article information

Source
Electron. J. Statist., Volume 14, Number 1 (2020), 1075-1136.

Dates
Received: March 2019
First available in Project Euclid: 26 February 2020

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1582686016

Digital Object Identifier
doi:10.1214/20-EJS1685

Subjects
Primary: 62M09: Non-Markovian processes: estimation 62F12: Asymptotic properties of estimators

Keywords
fractional Brownian motion parameter drift estimation ergodicity

Rights
Creative Commons Attribution 4.0 International License.

Citation

Panloup, Fabien; Tindel, Samy; Varvenne, Maylis. A general drift estimation procedure for stochastic differential equations with additive fractional noise. Electron. J. Statist. 14 (2020), no. 1, 1075--1136. doi:10.1214/20-EJS1685. https://projecteuclid.org/euclid.ejs/1582686016


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