On inference for fractional differential equations

Alexandra Chronopoulou (1) , Samy Tindel (2, 1)

1 BIGS - Biology, genetics and statistics
2 IECL - Institut Élie Cartan de Lorraine

Based on Malliavin calculus tools and approximation results, we show how to compute a maximum likelihood type estimator for a rather general differential equation driven by a fractional Brownian motion with Hurst parameter H>1/2. Rates of convergence for the approximation task are provided, and numerical experiments show that our procedure leads to good results in terms of estimation.

Mots clés: Malliavin calculus; Fractional Brownian motion; Stochastic differential equations; Inference for stochastic processes

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

Alexandra Chronopoulou, Samy Tindel. On inference for fractional differential equations. Statistical Inference for Stochastic Processes, 2013, 16 (1), pp.29-61. ⟨10.1007/s11203-013-9076-z⟩. ⟨hal-00587087⟩