Estimation of the Brownian dimension of a continuous Ito process

In this paper, we consider a d-dimensional continuous Ito process which is observed at it regularly spaced times on it 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, all similar to asymptotic testing hypotheses.