2021/06/18 by Andrey Pilipenko, Pilipenko, Andrey, Frank Proske +1
Computer Science · Economics, Econometrics and Finance · Mathematics · #49N60 #60H10 #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #Probability (math.PR) #Stochastic processes and financial applications #Stochastic processes and statistical mechanics
paper · pdf · doi:10.48550/arxiv.2106.09935
openalex publication_date 2021/06/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we study zero-noise limits of α-stable noise perturbed ODE's which are driven by an irregular vector field A with asymptotics % A(x)∼ a((x)/(\vert x\vert ))\vert x\vert β-1x at zero, where a>0 is a continuous function and β∈ (0,1). The results established in this article can be considered a generalization of those in the seminal works of Bafico \citeBa and Bafico, Baldi \citeBB to the multi-dimensional case. Our approach for proving these results is inspired by techniques in \cite% PPselfsimilar and based on the analysis of an SDE for t\longrightarrow ∞ , which is obtained through a transformation of the perturbed ODE.