A uniform estimate for rough paths (Q390507)

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.