Estimation of the Brownian dimension of a continuous Ito process

Jean Jacod (1) , Antoine Lejay (2, 3) , Denis Talay (3)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires
2 IECN - Institut Élie Cartan de Nancy
3 TOSCA - Simuler et calibrer des modèles stochastiques

In this paper we consider a d-dimensional continuous Ito process, which is observed at n regularly spaced times on a given time interval [0,T]. This process is driven by a multidimensional Wiener process, and our aim is to provide asymptotic statistical procedures which give the minimal dimension of the driving Wiener process, which is between 0 (a pure drift) and d. We exhibit several different procedures, which are all similar to asymptotic testing hypotheses.

Mots clés: brownian dimension; stochastic differential equation; calibration of diffusion process

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

Jean Jacod, Antoine Lejay, Denis Talay. Estimation of the Brownian dimension of a continuous Ito process. Bernoulli, 2008, 14 (2), pp.469-498. ⟨10.3150/07-BEJ6190⟩. ⟨inria-00143541v2⟩