不精确信息下常微分方程的随机Euler格式
On the randomized Euler schemes for ODEs under inexact information
摘要：
分析了随机显式和隐式Euler格式近似求解常微分方程的误差。我们考虑一类常微分方程的右端函数满足利普希茨条件的整体或仅局部。此外，我们假设只有不精确的离散信息，被一些噪声破坏，关于右手边的功能是可用的。研究了显式和隐式随机欧拉算法的最优性和稳定性。
英文摘要：
We analyse errors of randomized explicit and implicit Euler schemes for approximate solving of ordinary differential equations (ODEs). We consider classes of ODEs for which the right-hand side functions satisfy Lipschitz condition globally or only locally. Moreover, we assume that only inexact discrete information, corrupted by some noise, about the right-hand side function is available. Optimality and stability of explicit and implicit randomized Euler algorithms are also investigated.
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