On a relation between stochastic integration and geometric measure theory

Franco Flandoli, Mariano Giaquinta, Massimiliano Gubinelli and Vincenzo M. Tortorelli

First issued 29 November 2002 · PDF

Abstract

Two problems are addressed for the path of certain stochastic processes: a) do they define currents? b) are these currents of a classical type? A general answer to question a) is given for processes like semimartingales or with Lyons-Zheng structure. As to question b), it is shown that Hölder continuous paths with exponent $\gamma > 1/2$ define integral flat chains.

Versions

1. Version 1 (arXiv v1) current
   29 November 2002
   arXiv comments: 30 pages, no figures
   PDF · LaTeX source · files and digests · arXiv:math/0211458

Cite

Franco Flandoli, Mariano Giaquinta, Massimiliano Gubinelli and Vincenzo M. Tortorelli. On a relation between stochastic integration and geometric measure theory. Papers of Massimiliano Gubinelli, 2002, version 1. https://mgubi.org/papers/paper/stochastic-currents/

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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