On regularization by a small noise of multidimensional ODEs with non-Lipschitz coefficients

• Date: 2020
• Main Authors: Pilipenko, A., Kulik, A.
• Format: Article
• Language: Ukrainian
• Published: Institute of Mathematics, NAS of Ukraine 2020
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/6292
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

UDC 519.21 In this paper we solve a selection problem for multidimensional SDE $d X^{\epsilon}(t)=a(X^{\epsilon}(t))\, d t + \epsilon\sigma(X^{\epsilon}(t))\, d W(t),$ where the drift and diffusion are locally Lipschitz continuous outside of a fixed hyperplane $H.$It is assumed that $X^{\epsilon}(0)...