Geodesic
On the completeness of stochastic flows generated by equations with current velocities
Teoriâ veroâtnostej i ee primeneniâ, Tome 64 (2019) no. 1, pp. 3-16

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Sufficient conditions as well as necessary and sufficient ones are found for the completeness of the stochastic flow generated by equations with the so-called current velocities (Nelson's symmetric mean derivatives). A characteristic property of such equations is that the solvability of the Cauchy problem (the existence of orbits of the flow) is proved only under the assumption that the initial value is a random variable such that its distribution density is smooth and nowhere vanishes.
Keywords: mean derivatives, current velocities, stochastic flows, completeness, continuity at infinity. 
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     author = {Yu. E. Gliklikh and T. A. Shchichko},
     title = {On the completeness of stochastic flows generated by equations with current velocities},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
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     number = {1},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2019_64_1_a0/}
}
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Yu. E. Gliklikh; T. A. Shchichko. On the completeness of stochastic flows generated by equations with current velocities. Teoriâ veroâtnostej i ee primeneniâ, Tome 64 (2019) no. 1, pp. 3-16. http://geodesic.mathdoc.fr/item/TVP_2019_64_1_a0/