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Lévy’s area under conditioning. (English) Zbl 1099.60054
The authors give an estimation, for \(\alpha\in(0,1)\), of the \(\alpha\)-Hölder norm of a \(d\)-dimensional Brownian motion and its Lévy stochastic area, conditional on the Brownian path being uniformly small. The result is of interest in the analysis of stochastic integral equations via the theory of ‘rough paths’.

MSC:
60J65 Brownian motion
60G15 Gaussian processes
60H05 Stochastic integrals
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