Some Feller and Osgood type criteria for semilinear stochastic differential equations.

By means of Itô's formula and a comparison theorem for integral equations, we study the blow up in finite time of semilinear stochastic differential equations of the form Here, is non-negative and non-decreasing by components, is a predictable and continuous process, is an -Brownian motion and is an -measurable random variable. The results of this paper can be seen as extensions of the Feller and Osgood criteria. [ABSTRACT FROM AUTHOR]