A note on the probabilistic stability of randomized Taylor schemes

[摘要] 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.

[学科分类] 数学（综合）

[关键词] randomized Taylor schemes;mean-square stability;asymptotic stability;stability in probability