Geodesic
One dimensional stochastic differential equations: pathwise approach
Ufa mathematical journal, Tome 5 (2013) no. 4, pp. 3-15

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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. 
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M. A. Abdullin; N. S. Ismagilov; F. S. Nasyrov. One dimensional stochastic differential equations: pathwise approach. Ufa mathematical journal, Tome 5 (2013) no. 4, pp. 3-15. http://geodesic.mathdoc.fr/item/UFA_2013_5_4_a0/