On Asymptotic Behavior of Stochastic Differential Equation Solutions in Multidimensional Space

2023/06/03 by Viktor Yuskovych, Yuskovych, Viktor
Computer Science · Economics, Econometrics and Finance · Mathematics · #Advanced Mathematical Modeling in Engineering #Differential Equations and Numerical Methods #FOS: Mathematics #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2306.02089

openalex publication_date 2023/06/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 → ∞, 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.

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