Controlling Rough Paths

Massimiliano Gubinelli

First issued 30 June 2003 · PDF

Abstract

We formulate indefinite integration with respect to an irregular function as an algebraic problem and provide a criterion for the existence and uniqueness of a solution. This allows us to define a good notion of integral with respect to irregular paths with Hoelder exponent greater than 1/3 (e.g. samples of Brownian motion) and study the problem of the existence, uniqueness and continuity of solution of differential equations driven by such paths. We recover Young's theory of integration and the main results of Lyons' theory of rough paths in Hoelder topology.

Versions

1. Version 2 (arXiv v2) current
   28 October 2003
   arXiv comments: 43 pages, no figures, corrected a proof in Sec. 6
   PDF · LaTeX source · files and digests · arXiv:math/0306433
2. Version 1 (arXiv v1)
   30 June 2003
   arXiv comments: 41 pages, no figures
   PDF · LaTeX source · files and digests · arXiv:math/0306433

Cite

Massimiliano Gubinelli. Controlling Rough Paths. Papers of Massimiliano Gubinelli, 2003, version 2. https://mgubi.org/papers/paper/controlling-rough-paths/

Licence: arXiv.org non-exclusive license to distribute, assumed for submissions of 1991-2003; all other rights reserved to the authors

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