Sufficient condition for the existence of explosive solutions for stochastic differential equation

In this paper, we discuss the existence condition for explosive solutions of stochastic differential equations (SDEs). In contrast to the classical Osgood condition respect to drift coefficients of ordinary differential equations (ODEs), our paper proposes a similar Osgood condition with respect to the diffusion coefficient. Finally, we illustrate the correctness of the paper’s conclusions by giving some representative examples and thereby showing that our conclusions extend some results in existing literature.