随机微分方程的有限时间爆炸：Khasminskii Lyapunov方法及其与Osgood准则一致性的综述
Finite Time Explosion of Stochastic Differential Equations: A survey into Khasminskii's Lyapunov Method and its Consistency with the Osgood Criterion
AI总结：
本文综述Khasminskii Lyapunov方法如何分类随机微分方程解的三类有限时间爆炸行为，并结合Feller检验、示例及向常数Poisson强度跳过程的扩展说明其适用性。
摘要：
随机微分方程的解可能具有三类爆炸行为：几乎必然不爆炸、以正概率爆炸以及几乎必然爆炸。本文将综述用于分类随机微分方程解的爆炸行为的Khasminskii Lyapunov方法。我们将从考察著名的Feller爆炸检验并观察其不足开始这一探索。随后，我们将介绍针对几乎必然不爆炸、以正概率爆炸和几乎必然爆炸的Khasminskii Lyapunov方法。文中将提供大量示例，以阐明Khasminskii Lyapunov方法的效力。此外，本文还会作简要延伸，把用于几乎必然不爆炸和以正概率爆炸的Khasminskii Lyapunov方法推广到具有常数Poisson强度的跳过程。
英文摘要：
Solutions of Stochastic Differential Equations can have three types of explosive behaviors: almost-sure non-explosive, explosion with positive probability, and almost sure explosion. In this paper, we will provide a survey of Khasminskii's Lyapunov method for classifying explosive behaviors of solutions of stochastic differential equations. We will embark our expedition by examining the renowned Feller's test for explosion and observing its shortfalls. Afterwards, we will present Khasminskii's Lyapunov method for almost-sure non-explosion, explosion with positive probability, and almost-sure explosion. Ample examples will be provided to illuminate the power of Khasminskii's Lyapunov methods. Furthermore, quick layovers will be made to extend Khasminskii's Lyapunov method for almost-sure non-explosion and explosion with positive probability for jump processes with constant Poisson intensities.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
