主讲人简介：

John Andrew Appleby，都柏林城市大学数学科学系教授，博士生导师，出版专著4部，发表论文60余篇。研究领域：随机微分方程。

内容摘要：

Theorems of Hartman--Wintner type in the theory of differential equations typically consider perturbed linear equations, and determine conditions under which thesolution of the perturbed equation is asymptotic to the solution of the unperturbed equation. In this talk, we concentrate on equations with growing solutions. First, we give conditions under which Hartman--Wintner results canbe extended to sublinear ordinary differential equations. Second, for super linear differential equations, Hartman--Wintner results are unsuitable, sowe establish results which may be thought of as extensions of Bihari'sinequality. In both cases, we demonstrate that our conditions are sharp, or even necessary and sufficient. The results are applied to determine the exact asymptotic behaviour of sublinear and super linear stochastic differential equations, including a process we call subexponential Brownian motion.

讲座主持：胡良剑  教授

讲座语言：英语