Flows driven by rough paths

Details Flows driven by rough paths Flows driven by rough paths

2012-03-05

arxiv.org/abs/1203.0888v4

Mathematics

Probability

v4, 30 pages. Minor improvements in the presentation. Typos corrected -- especially in theorem 33, hypothesis (6.3), on mean f

Scientific paper

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.

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