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Trees and rough paths

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Each real-valued continuous path defined on [0,1] can be associated to a tree. Our aim is to discuss the relationship between these two objects. It turns out that some properties of the path, such that the fact that it has finite p-variation, can be translated into a geometric property of the tree. Moreover, integrals with respect to the path can be written as integrals on the tree; this can be done for the Young integral but also for some integrals of the rough paths theory. This approach can be applied to stochastic paths such as fractional Brownian motions in order to construct stochastic integrals.

This talk is part of the Probability series.

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