An Osgood's criterion for a semilinear stochastic differential equation

Abstract

The purpose of this paper is to give an Osgood's criterion for solutions of semilinear stochastic differential equations of the form $X_t=\xi +{\int }_0^{t}b(s,X_s)ds+{\int }_0^t\sigma (s)X_{s}d{W}_s,t\ge 0$. 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 $\sigma \equiv 1$.

arXiv comment21 pages

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