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Convergence rates for the full Brownian rough paths with applications to limit theorems for stochastic flows. (English) Zbl 1237.60044
A quantitative version of a well-known limit theorem is presented. It says, in essence, that if one uses piecewise linear approximations to multidimensional Brownian driving signals, the resulting solutions to the (random) ODEs will converge as stochastic flows to the solution of the (Stratonovich) stochastic differential equations; that is, the solution flows and all their derivatives will convergence uniformly on compacts. Rough path theory is used to prove limit theorems relying on refined Hölder metrics on rough path spaces. The convergence for the full Brownian rough path involves five lemmas and two theorems. The paper is addressing highly specialized researchers dealing with stochastic analysis.

MSC:
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)
60H05 Stochastic integrals
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