Homeomorphic flows for multi-dimensional SDEs with non-Lipschitz coefficients

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Flow of diffeomorphisms for SDEs with unbounded H (2009, methodology): “Strong completeness for non-locally Lipschitz coefficients can be established replacing the global Lipschitz condition on the coefficients with global log-Lipschitz type conditions (see [27,31,9,8]).”
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.).”
Freidlin–Wentzell's large deviations for homeomorphism flows of non-Lipschitz SDEs (2005, unknown): “The present work is motivated by the fundamental paper of Airault, Malliavin and Thalmaier [1] which in particular constructs the Brownian motion on the diffeomorphism group of the disc, and the recent work of one of the authors [9] in which stochastic flows of stochastic differential equations with”
Well-posedness of the transport equation by stochastic perturbation (2008, background): “For papers that tackle existence of global flows of homeomorphisms for SDEs without global Lipschitz coefficients see [37, 11] and the references therein.”