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Differential equations driven by rough paths: An approach via discrete approximation. (English) Zbl 1163.34005
Author’s abstract: A theory of systems of differential equations of the form
\[ dy^i = \sum_jf^i_j(y)dx^i, \] where the driving path \(x(t)\) is nondifferentiable, has recently been developed by Lyons. I develop an alternative approach to this theory, using (modified) Euler approximations, and investigate its applicability to stochastic differential equations driven by Brownian motion. I also give some other examples showing that the main results are reasonably sharp.

MSC:
34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
34F05 Ordinary differential equations and systems with randomness
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