The purpose of this paper is to give an Osgood's criterion for solutions of semilinear stochastic differential equations of the form $X_{ t}=\xi +\int_{ 0}^{ t}b(s,X_{ s})ds+\int_{ 0}^{ t}\sigma (s)X_{ s}dW_{ s},\ t\geq 0$. Here, $b$ is a non-negative, non-decreasing by components and continuous random field and $\sigma $ is a predictable and continuous process. Also we present a generalization of the so-called Feller's test whenever $\sigma \equiv 1$.
Categories: math.PR
