Flows driven by rough paths
Résumé
We show in this work how the familiar Taylor formula can be used in a simple way to reprove from scratch the main existence and well-posedness results from rough paths theory; the explosion question, convergence of Euler schemes and Taylor expansion are also dealt with. Unlike other approaches, we work mainly with flows of maps rather than with paths. We illustrate our approach by proving a well-posedness result for some mean field stochastic rough differential equation.