Flows driven by rough paths
By Ismaël F. Bailleul. 2012
70 citations recorded by the source corpus.
We devise in this work a simple mechanism for constructing flows on a Banach space from approximate flows, and show how it can be used in a simple way to reprove from scratch and extend the main existence and well-posedness results for rough differential equations, in the context of dynamics on a Banach space driven by a Holder weak geometric rough path; the explosion question under linear growth conditions, Taylor expansion and Euler estimates are also dealt with. We illustrate our approach by proving an existence and well-posedness result for some mean field stochastic rough differential equation.
Subfields: Computational Theory and Mathematics, Finance, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/8c09b6b0eee7136f2d6f94d30d970017a4b5cfeb
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Citations in the corpus
- Rough differential equations with unbounded drift term (2016, background): “ooth!) path x: [0,∞) → R2 and show that the solution to (0.1) explodes in finite time. This suggests the need to impose an additional condition on bwhich controls the growth in tangential 2In fact, in [Bai15], the flow is even the central object of interest and it is constructed directly, skipping the”