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A general drift estimation procedure for stochastic differential equations with additive fractional noise. (English) Zbl 1439.62186

Summary: 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.

MSC:

62M09 Non-Markovian processes: estimation
62F12 Asymptotic properties of parametric estimators
60G22 Fractional processes, including fractional Brownian motion
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
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