On asymptotic behavior of solutions of stochastic differential equations in multidimensional space

Abstract

Consider the multidimensional SDE dX(t) = a(X(t)) dt + b(X(t)) dW(t). We study the asymptotic behavior of its solution X(t) as t → ∞, namely, we study sufficient conditions of transience of its solution X(t), stabilization of its multidimensional angle X(t)/|X(t)|, and asymptotic equivalence of solutions of the given SDE and the following ODE without noise: dx(t) = a(x(t)) dt.