K. Chouk and M. Gubinelli
Rough sheets are two-parameter analogs of rough paths. In this work the theory of integration over functions of two parameters is extended to cover the case of irregular functions by developing an appropriate notion of rough sheet. The main application is to give a path by path construction of the stochastic integral in the plane and obtain a stratonovich change of variables formula.
K. Chouk and M. Gubinelli. Rough sheets. Papers of Massimiliano Gubinelli, 2014, version 1. https://mgubi.org/papers/paper/rough-sheets/
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