Estimation of the Brownian dimension of a continuous Itô process

Details Estimation of the Brownian dimension of a continuous Itô process Estimation of the Brownian dimension of a continuous Itô process

2008-05-14

arxiv.org/abs/0805.2072v1

Bernoulli 2008, Vol. 14, No. 2, 469-498

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.3150/07-BEJ6190 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statist

Scientific paper

10.3150/07-BEJ6190

In this paper, we consider a $d$-dimensional continuous It\^{o} 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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