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Statistics & Risk Modeling

with Applications in Finance and Insurance

Editor-in-Chief: Stelzer, Robert

Cite Score 2018: 0.85

SCImago Journal Rank (SJR) 2018: 0.354
Source Normalized Impact per Paper (SNIP) 2018: 0.604

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Estimating the dimension of factors of diffusion processes

Klaus Pötzelberger
Published Online: 2009-09-25 | DOI: https://doi.org/10.1524/stnd.


We present consistency results for estimators of the box-counting dimension of the support of probability distributions. The box-counting dimension of the support E is defined via the covering number, i.e. the minimal cardinality of a cover of E consisting of cubes of fixed side-length. Accordingly the covering number of a sample allows the definition of an estimator of the box-counting dimension of E. Consistency results for arrays of probability distributions may be applied to the distributions of innovations of Itô processes and allow the construction of consistent estimators of the dimension of the factors, i.e. of the dimension of the Brownian motion driving the process.

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Published Online: 2009-09-25

Published in Print: 2003-02-01

Citation Information: Statistics & Decisions/International mathematical Journal for stochastic methods and models, Volume 21, Issue 2/2003, Pages 171–184, ISSN (Print) 0721-2631, DOI: https://doi.org/10.1524/stnd.

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