Estimation of the Brownian dimension of a continuous Ito process

http://isi.cbs.nl/bernoulli/International audienceIn 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