On a relation between stochastic integration and geometric measure theory

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

On a relation between stochastic integration and geometric measure theory

Authors

Flandoli, Franco

Giaquinta, Mariano

Gubinelli, Massimiliano

Tortorelli, Vincenzo M.

Description

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 $γ> 1/2$ define integral flat chains.
30 pages, no figures