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

TL;DR

This paper develops criteria for existence, uniqueness, extinction, explosion, and contractivity of solutions to time-inhomogeneous SDEs with jumps, extending previous results and applying to mean field SDEs.

Contribution

It provides new generalized criteria for solution behaviors of complex SDEs with jumps, including mean field cases.

Findings

Criteria for existence and uniqueness of solutions.

Conditions for extinction and explosion.

Analysis of contractivity properties.

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.