Construction of Flows through the Non-Linear Sewing Lemma II

Abstract: The theory of rough paths is now a vivid field of research at the intersection of many domains such as analysis (stochastic and classical), algebra, geometry, data science and so on. Its first objective was to construct integrals and differential equations driven by irregular signal, before expanding in many directions.

The various interpretations of this theory all rely on variants of the so-called sewing lemma. In this talk, we consider how to construct directly flows from numerical schemes using a "non-linear sewing lemma”, and present some of the main properties that can be reached. We put them in parallel with some results in the theory of ordinary differential equations and show how they are expanded.

A second part will be devoted to the relationship between such flows and other objects already existing in the theory of rough paths.

From a joint work with A. Brault.

differential geometryprobability

Audience: advanced learners

Young Researchers between Geometry and Stochastic Analysis 2021