Modulus of continuity of the canonic Brownian motion “on the group of diffeomorphisms of the circle”

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Stochastic flows of SDEs with irregular coefficients and stochastic transport equations (2009, background): “Recently, there are increasing interests for studying the stochastic homeomorphism flow property associated with SDE (1.1) under variousnon-Lipschitz assumptions onb andσ (cf. [21, 1, 20, 25, 8, 9, 10, 11, 28], etc.).”
Flows, coalescence and noise (2002, methodology): “It is known that, as a separable compact metric space, M is homeomorphic to a closed subset of [0, 1]N (see corollaire 1 6.”