We study the stability of randomized Taylor schemes for ODEs. We consider three notions of probabilistic stability: asymptotic stability, mean-square stability, and stability in probability. We prove fundamental properties of the probabilistic stability regions and benchmark them against the absolute stability regions for deterministic Taylor schemes.

翻译：我们研究了常微分方程随机泰勒格式的稳定性。我们考虑了概率稳定性的三个概念：渐进稳定性、均方稳定性和概率稳定性。我们证明了概率稳定性区域的基本性质，并将其与确定性泰勒格式的绝对稳定性区域进行了基准比较。