Yet Another Introduction to Rough Paths
نویسنده
چکیده
This article provides another point of view on the theory of rough paths, which starts with simple considerations on ordinary integrals, and endows the importance of the Green-Riemann formula, as in the work of D. Feyel and A. de La Pradelle. This point of view allows us to introduce gently the required algebraic structures and provides alternative ways to understand why the construction of T. Lyons et al. is a natural generalization of the notion of integral of differential forms, in the sense it shares the same properties as integrals along smooth paths, when we use the “right notion” of path.
منابع مشابه
An Introduction to Rough Paths
Abstract: This article aims to be an introduction to the theory of rough paths, in which integrals of differential forms against irregular paths and differential equations controlled by irregular paths are defined. This theory makes use of an extension of the notion of iterated integrals of the paths, whose algebraic properties appear to be fundamental. This theory is well-suited for stochastic...
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