Almost sure explosion of solutions to stochastic differential equations

作者：Chow Pao Liu^*; Khasminskii Rafail

来源：Stochastic Processes and Their Applications, 2014, 124(1): 639-645.

DOI：10.1016/j.spa.2013.09.006

• Stochastic differential equation
• Ito's formula
• Explosive solutions
• Lyapunov function
• Cycle

This paper is concerned with the problem of explosive solutions for a class of stochastic differential equations. Our main results are presented as two theorems. Theorem 1 is concerned with the existence of explosive solutions with positive probability under certain sufficient conditions. With some additional mild conditions, it is shown in Theorem 2 that the explosion will occur almost surely. The methods of auxiliary functions and cycles are used in the proofs. Several remarks about their applications are given.

• 出版日期2014-1