Geodesic
On solvability of stochastic differential equations with osmotic velocities
Teoriâ veroâtnostej i ee primeneniâ, Tome 65 (2020) no. 4, pp. 806-817

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We give conditions such that solutions exist of the stochastic equation with the so-called osmotic velocities (the so-called Nelson's antisymmetric mean derivatives). We show that the solutions may not exist. Specifically, initial conditions are determined by the right-hand sides; however, some right-hand sides do not determine initial conditions, and in this case the solutions do not exist. Moreover, under the “correct” initial condition the solution is shown to be nonunique.
Keywords: mean derivatives, osmotic velocities, equations with osmotic velocities
Mots-clés : existence of solutions. 
@article{TVP_2020_65_4_a7,
     author = {Yu. E. Gliklikh},
     title = {On solvability of stochastic differential equations with osmotic velocities},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {806--817},
     publisher = {mathdoc},
     volume = {65},
     number = {4},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2020_65_4_a7/}
}
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Yu. E. Gliklikh. On solvability of stochastic differential equations with osmotic velocities. Teoriâ veroâtnostej i ee primeneniâ, Tome 65 (2020) no. 4, pp. 806-817. http://geodesic.mathdoc.fr/item/TVP_2020_65_4_a7/