Flows driven by rough paths | Zendy

Ismaël Bailleul | Zendy

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Flows driven by rough paths

Author(s) -

Ismaël Bailleul

Publication year - 2015

Publication title -

revista matemática iberoamericana

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.569

H-Index - 52

eISSN - 2235-0616

pISSN - 0213-2230

DOI - 10.4171/rmi/858

Subject(s) - banach space , mathematics , simple (philosophy) , context (archaeology) , stochastic differential equation , space (punctuation) , mathematical analysis , path (computing) , computer science , paleontology , philosophy , epistemology , programming language , biology , operating system

v4, 30 pages. Minor improvements in the presentation. Typos corrected -- especially in theorem 33, hypothesis (6.3), on mean field stochastic rough differential equation. SubmittedInternational audienceWe 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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