This article is cited in 6 papers

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On existence of solutions to stochastic differential equations with current velocities

S. V. Azarina^a, Yu. E. Gliklikh<sup>b

a</sup> Kuban State University, Krasnodar, Russian Federation
^b Voronezh State University, Voronezh, Russian Federation

Abstract: The notion of mean derivatives was introduced by E. Nelson in 60-th years of XX century and at the moment there are a lot of mathematical models of physical processes constructed in terms of those derivatives. The paper is devoted to investigation of stochastic differential equations with current velocities, i.e., with Nelson's symmetric mean derivatives. Since the current velocities of stochastic processes are natural analogues of ordinary physical velocities of deterministic processes, such a research is important for investigation of models of physical processes that take into account stochastic properties. An existence of solution theorem for those equations is obtained.

Keywords: mean derivatives; equations with current velocities; existence and uniqueness of solutions.

UDC: 517.9+519.216.2

MSC: 60H10, 60H30, 60K30

Received: 21.05.2015

Language: English

DOI: 10.14529/mmp150408

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