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arXiv · 1902.11010

A numerical method for solving stochastic differential equations with noisy memory

Kristina Rognlien Dahl
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Abstract

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 $\sqrt{\Delta t}$. 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.

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Kristina Rognlien Dahl. 2019-02-28. A numerical method for solving stochastic differential equations with noisy memory. https://arxiv.org/abs/1902.11010

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