TL;DR
This paper extends rough path theory to two-parameter functions, introducing rough sheets to define integrals over irregular functions in the plane and establishing a Stratonovich change of variables formula.
Contribution
It develops the concept of rough sheets, a two-parameter analog of rough paths, enabling stochastic integration in the plane with irregular functions.
Findings
Introduces the notion of rough sheets for two-parameter functions.
Provides a path-by-path construction of stochastic integrals in the plane.
Establishes a Stratonovich change of variables formula for rough sheets.
Abstract
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.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Rough Sets and Fuzzy Logic · Advanced Numerical Analysis Techniques