In this paper we present a new method for deriving Itô stochastic delay differential equations (SDDEs) from delayed chemical master equations (DCMEs). Considering alternative formulations of SDDEs that can be derived from the same DCME, we prove that they are equivalent both in distribution, and in sample paths they produce. This allows us to formulate an algorithmic approach to deriving equivalent Itô SDDEs with a smaller number of noise variables, which increases the computational speed of simulating stochastic delayed systems. The new method is illustrated on a simple model of two interacting species, and it shows excellent agreement with the results of direct stochastic simulations, while also demonstrating a much superior speed of performance.

中文翻译：

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一种模拟随机时滞系统的新方法。

在本文中，我们提出了一种从延迟化学主方程（DCME）推导Itô随机延迟微分方程（SDDE）的新方法。考虑到可以从同一DCME衍生的SDDE的替代配方，我们证明了它们在分布和产生的样品路径上都是等效的。这使我们能够制定一种算法方法，以推导具有较少数量噪声变量的等效ItôSDDE，从而提高了模拟随机延迟系统的计算速度。在两个相互作用物种的简单模型上说明了该新方法，它与直接随机模拟的结果显示出极好的一致性，同时还展示了更高的性能速度。