ABSTRACT
There are a number of reasons why one may want to estimate multifractal characteristics of a probability measure . Many of the measures of location, spread and so on that are used to characterise classical probability distributions are not useful when the probability measure contains singularities of possibly many different orders. If a probability measure has singularities, possibly of many different orders, then one possibility is to characterise it on the basis of its singularities. The multifractal spectrum is one way to describe the sizes of subsets of X containing singularities of a given order. However, the multifractal spectrum is difficult to deal with numerically, and hence one usually estimates the Re´nyi dimensions, and then calculates the Legendre transform to produce the multifractal spectrum (Chapter 2).
