Controlling Rough Paths
Probability
2007-05-23 v2
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.
Keywords
Cite
@article{arxiv.math/0306433,
title = {Controlling Rough Paths},
author = {Massimiliano Gubinelli},
journal= {arXiv preprint arXiv:math/0306433},
year = {2007}
}
Comments
43 pages, no figures, corrected a proof in Sec. 6