A tree approach to $p$-variation and to integration

Details A tree approach to $p$-variation and to integration A tree approach to $p$-variation and to integration

2007-05-15

arxiv.org/abs/0705.2128v2

Annals of Probability 36, 6 (2008) 2235-2279

Mathematics

Probability

Scientific paper

10.1214/07-AOP388

We consider a real-valued path; it is possible to associate a tree to this path, and we explore the relations between the tree, the properties of $p$-variation of the path, and integration with respect to the path. In particular, the fractal dimension of the tree is estimated from the variations of the path, and Young integrals with respect to the path, as well as integrals from the rough paths theory, are written as integrals on the tree. Examples include some stochastic paths such as martingales, L\'evy processes and fractional Brownian motions (for which an estimator of the Hurst parameter is given).

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