This article is cited in 2 papers

Short Communications

On solvability of stochastic differential equations with osmotic velocities

Yu. E. Gliklikh

Voronezh State University

Abstract: 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, existence of solutions.

Received: 03.07.2019
Revised: 24.12.2019
Accepted: 22.01.2020

DOI: 10.4213/tvp5335

 English version: Theory of Probability and its Applications, 2021, 65:4, 640–647

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