This article is cited in 3 papers

One dimensional stochastic differential equations: pathwise approach

M. A. Abdullin, N. S. Ismagilov, F. S. Nasyrov

Ufa State Aviation Technical University, Ufa, Russia

Abstract: We study path-wise analogues of one dimensional stochastic differential equations with symmetric integrals. We find existence and uniqueness conditions for solutions, the conditions of continuity and differentiability w.r.t. a parameter, as well as the conditions of linearization for such equations. We also study the structure of the solutions.

Keywords: symmetric integral, differential equations with symmetric integral.

UDC: 519.216.73+519.216.71

MSC: 60H10, 60H05

Received: 24.08.2013

 English version: Ufa Mathematical Journal, 2013, 5:4, 3–15

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