Abstract
We prove the comparison theorems for scalar stochastic differential equations in the case of different diffusion coefficients. Conditions are given of stability with probability 1 with respect to the trivial solution to stochastic differential equations with random coefficients. The results remain valid for deterministic analogs of stochastic differential equations with symmetric integrals.
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Ufa. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 57, No. 5, pp. 969–977, September–October, 2016; DOI: 10.17377/smzh.2016.57.502.
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Asylgareev, A.S., Nasyrov, F.S. Theorems of comparison and stability with probability 1 for one-dimensional stochastic differential equations. Sib Math J 57, 754–761 (2016). https://doi.org/10.1134/S0037446616050025
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DOI: https://doi.org/10.1134/S0037446616050025