The graph of a Gaussian stochastic process, regarded as a subset of the plane, has a fractal dimension lying between 1 and 2. The fractal dimension depends on the underlying smoothness of the process, with smoother processes having a lower dimension. A simple and natural estimate of the fractal dimension can be constructed from n equally-spaced observations, with the observations becoming more finely-spaced as n increases. It is natural to expect the variance of this estimator to have variance of order 1/n as n increases. However, this property holds only if the underlying process is sufficiently rough. In this talk we shall explore why the accuracy of the estimator deteriorates if the underlying process is too smooth, and we propose a family of new estimators which do have the desired accuracy.

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If you require further information please contact Charles Taylor

e-mail: charles@maths.leeds.ac.uk