Estimation of the Brownian dimension of a continuous Ito process

Jean Jacod 1 Antoine Lejay 2, 3 Denis Talay 3
3 TOSCA
INRIA Lorraine, CRISAM - Inria Sophia Antipolis - Méditerranée , UHP - Université Henri Poincaré - Nancy 1, Université Nancy 2, INPL - Institut National Polytechnique de Lorraine, CNRS - Centre National de la Recherche Scientifique : UMR7502
Abstract : 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.
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Jean Jacod, Antoine Lejay, Denis Talay. Estimation of the Brownian dimension of a continuous Ito process. Bernoulli, Bernoulli Society for Mathematical Statistics and Probability, 2008, 14 (2), pp.469-498. ⟨10.3150/07-BEJ6190⟩. ⟨inria-00143541v2⟩

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