Extinction, explosion and contraction for time-inhomogeneous SDEs with jumps

Abstract

For a class of time-inhomogeneous SDEs with jumps, we establish criteria for the existence and uniqueness of the nonnegative solutions, and examine the extinction, the explosion together with the contractivity of the solutions, which generalize and improve upon earlier results in the literature. As an application, we study the aforementioned properties for a class of mean field SDEs.