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.
Highlights
Let B be a d-dimensional fractional Brownian motion with Hurst parameter H ∈ (0, 1) defined on a complete probability space (Ω, F, P)
We label some basic results about equation (2.7) and its invariant measure for further use
We first recall some ergodic properties of stochastic differential equations driven by a fBm, we study the continuity of the invariant measure νθ with respect to the parameter θ
Summary
To cite this version: Fabien Panloup, Samy Tindel, Maylis Varvenne. Electronic Journal of Statistics , Shaker Heights, OH : Institute of Mathematical Statistics, 2020, 14 (1), pp.1075-1136. HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés. A GENERAL DRIFT ESTIMATION PROCEDURE FOR STOCHASTIC DIFFERENTIAL EQUATIONS WITH ADDITIVE FRACTIONAL NOISE
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