Estimation of the Brownian dimension of a continuous Itô process

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In this paper, we consider a d-dimensional continuous Itô 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, all similar to asymptotic testing hypotheses.