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Almost sure explosion of solutions to stochastic differential equations

Authors
Journal
Stochastic Processes and their Applications
0304-4149
Publisher
Elsevier
Volume
124
Issue
1
Identifiers
DOI: 10.1016/j.spa.2013.09.006
Keywords
  • Stochastic Differential Equation
  • Itô’S Formula
  • Explosive Solutions
  • Lyapunov Function
  • Cycle
Disciplines
  • Mathematics

Abstract

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.

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