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A uniform estimate for rough paths. (English) Zbl 1296.60155

The authors prove that for two rough paths all levels of their iterated integrals are close in a uniform sense if the first \(\lfloor p \rfloor\) levels are close. This explicit estimate is dimension-free and involves the \(p\)-variation of the rough paths and the uniform distance between the first \(\lfloor p \rfloor\) terms. The presented result is a weakening of a well known analogous result in which the \(p\)-variation instead of the uniform distance is used. As an example, the authors apply their result to the estimation of the difference of solutions to two rough linear differential equations.

MSC:

60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
34F05 Ordinary differential equations and systems with randomness
60G15 Gaussian processes
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References:

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