Geodesic
On solvability of stochastic differential equations with osmotic velocities
Teoriâ veroâtnostej i ee primeneniâ, Tome 65 (2020) no. 4, pp. 806-817 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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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/

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