A note on the probabilistic stability of randomized Taylor schemes

05/22/2022

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by   Tomasz Bochacik, et al.

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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.