Rough functions: \(p\)-variation, calculus, and index estimation (Q926643)

The author gives an overview of several dissipated results on the \(p\)-variation property of a function. Starting from the fact that a \(p\)-variation gives a convenient way to measure a degree of roughness of a function, the author attempts to show the usefulness of this property in a calculus of rough functions and to review boundedness of \(p\)-variation results for basic classes of stochastic processes. In the last section, two methods of estimating the \(p\)-variation index of a function given by finitely many values are discussed.