Estimation of the Brownian dimension of a continuous Itō process

Summary. 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