About stabilization by Poisson’s jumps for stochastic differential equations

Abstract

The well-known effect of stabilization by noise for Ito’s stochastic differential equations was proven by R.Z. Khasminskii more than 50 years ago. Here this effect is extended to stochastic differential equations with the Wiener process and Poisson’s measure. The obtained results are illustrated by examples with stabilization by Poisson’s jumps only or by white noise and Poisson’s jumps together. Some unsolved problem is proposed to the attention of readers.