具有噪声记忆的随机微分方程的数值方法
A numerical method for solving stochastic differential equations with noisy memory
AI总结：
本文提出了一种求解具有噪声记忆的随机微分方程的数值方法，通过推导Euler-Maruyama方案并证明其均方误差为Δt的平方根阶，展示了该方法在处理噪声记忆问题时的有效性。
摘要：
具有噪声记忆的随机微分方程通常无法解析求解。因此，本文推导了此类方程的数值Euler-Maruyama方案，并证明该方案的均方误差为Δt的平方根阶。这可能有些令人惊讶，因为尽管存在噪声记忆的复杂性，其阶数与常规SDE的Euler-Maruyama方案相同。为了说明该数值方法，我们将其应用于一个可以解析求解的噪声记忆SDE。
英文摘要：
Stochastic differential equations with noisy memory are often impossible to solve analytically. Therefore, we derive a numerical Euler-Maruyama scheme for such equations and prove that the mean-square error of this scheme is of order $\sqrt{Δt}$. This is, perhaps somewhat surprisingly, the same order as the Euler-Maruyama scheme for regular SDEs, despite the added complexity from the noisy memory. To illustrate this numerical method, we apply it to a noisy memory SDE which can be solved analytically.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
