On Asymptotic Behavior of Stochastic Differential Equation Solutions in Multidimensional Space
On Asymptotic Behavior of Stochastic Differential Equation Solutions in Multidimensional Space
复制标题
多维空间中随机微分方程解的渐近行为
DOI：
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发表时间：
2023
期刊：
影响因子：
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通讯作者：
V. Yuskovych
中科院分区：
文献类型：
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作者：
V. Yuskovych
考虑多维SDE $\mathrm d X(t) = a(X(t))\mathrm d t + b(X(t))\mathrm d W(t).$我们研究了其解$X(t)$的渐近行为为$t \to \infty$，即研究了其解$X(t)$的暂态性、多维角$X(t)/|X(t)|$的稳定性的充分条件，以及给定SDE与以下无噪声ODE解的渐近等价性： $\mathrm d x(t) = a(x(t))\mathrm d t.$
Consider the multidimensional SDE $\mathrm d X(t) = a(X(t))\mathrm d t + b(X(t))\mathrm d W(t).$ We study the asymptotic behavior of its solution $X(t)$ as $t \to \infty$, 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: $\mathrm d x(t) = a(x(t))\mathrm d t.$