Electronic Journal of Differential Equations,
Vol. 2007(2007), No. 140, pp. 1-9.

Title: Explosion time in stochastic differential equations with
       small diffusion

Authors: Pablo Groisman  (Univ. de Buenos Aires, Argentina)
         Julio D. Rossi  (Consejo Superior de Invest., Madrid, Spain)

Abstract: 
 We consider solutions of a one dimensional stochastic differential
 equations that explode in finite time. We prove that, under
 suitable hypotheses, the explosion time converges almost surely to
 the one of the ODE governed by the drift term when the diffusion
 coefficient approaches zero.

Submitted  June 21, 2007. Published October 19, 2007.
Math Subject Classifications: 60H10, 60G17, 34F05
Key Words: Explosion; stochastic differential equations.