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Preprints, Working Papers, ... Year : 2023

Parametric estimation of several parameters in discretely-observed Stochastic Differential Equations with additive fractional noise

Abstract

We investigate the problem of joint statistical estimation of several parameters for a stochastic differential equations driven by an additive fractional Brownian motion. Based on discrete-time observations of the model, we construct an estimator of the Hurst parameter, the diffusion parameter and the drift in a parametrised family of coercive drift coefficients. Our procedure is based on the assumption that the stationary distribution of the SDE and of its increments permit to identify the parameters of the model. We prove consistency results and derive a rate of convergence for the estimator under this assumption. Finally, we show that the identifiability assumption is satisfied in the case of a family of fractional Ornstein-Uhlenbeck processes and illustrate our results with some numerical experiments.
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Dates and versions

hal-04057186 , version 1 (04-04-2023)

Identifiers

  • HAL Id : hal-04057186 , version 1

Cite

El Mehdi Haress, Alexandre Richard. Parametric estimation of several parameters in discretely-observed Stochastic Differential Equations with additive fractional noise. 2023. ⟨hal-04057186⟩
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