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Differential equations with random perturbations are the
mathematical models of real-world processes that cannot be
described via deterministic laws, and their evolution depends on
random factors. The modern theory of differential equations with
random perturbations is on the edge of two mathematical
disciplines: random processes and ordinary differential equations.
Consequently, the sources of these methods come both from the
theory of random processes and from the classic theory of
differential equations. This work focuses on the approach to
stochastic equations from the perspective of ordinary differential
equations. For this purpose, both asymptotic and qualitative
methods which appeared in the classical theory of differential
equations and nonlinear mechanics are developed.
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