Almost sure explosion of solutions to stochastic differential equations

Pao-Liu Chow and Rafail Khasminskii

Stochastic Processes and their Applications, 2014, vol. 124, issue 1, 639-645

Abstract: 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.

Keywords: Stochastic differential equation; Itô’s formula; Explosive solutions; Lyapunov function; Cycle (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (5)

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DOI: 10.1016/j.spa.2013.09.006

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