A least square-type procedure for parameter estimation in stochastic differential equations with additive fractional noise

Andreas Neuenkirch (1) , Samy Tindel (2, 3)

1 Fachbereich Mathematik
2 IECN - Institut Élie Cartan de Nancy
3 BIGS - Biology, genetics and statistics

We study a least square-type estimator for an unknown parameter in the drift coefficient of a stochastic differential equation with additive fractional noise of Hurst parameter H>1/2. The estimator is based on discrete time observations of the stochastic differential equation, and using tools from ergodic theory and stochastic analysis we derive its strong consistency.

Mots clés: fractional Brownian motion; parameter estimation; least square procedure; ergodicity

Domaines: Probabilités [math.PR]; Statistiques [math.ST]; Théorie [stat.TH]

Andreas Neuenkirch, Samy Tindel. A least square-type procedure for parameter estimation in stochastic differential equations with additive fractional noise. 2011. ⟨hal-00639030⟩