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 [Formula: see text] Here, [Formula: see text] is non-negative and non-decreasing by components, [Formula: see text] is a predictable and continuous process, [Formula: see text] is an [Formula: see text]-Brownian motion and [Formula: see text] is an [Formula: see text]-measurable random variable. The results of this paper can be seen as extensions of the Feller and Osgood criteria.