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arXiv · 0805.2072

Estimation of the Brownian dimension of a continuous Itô process

Jean Jacod·Antoine Lejay·Denis Talay
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Abstract

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.

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Jean Jacod, Antoine Lejay, Denis Talay. 2008-05-14. Estimation of the Brownian dimension of a continuous Itô process. https://doi.org/10.3150/07-bej6190

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