This article is cited in 5 papers

On the completeness of stochastic flows generated by equations with current velocities

Yu. E. Gliklikh, T. A. Shchichko

Voronezh State University

Abstract: 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.

Received: 18.06.2018
Revised: 06.09.2018
Accepted: 18.10.2018

DOI: 10.4213/tvp5230

 English version: Theory of Probability and its Applications, 2019, 64:1, 1–11

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