WEAK ERROR ANALYSIS OF NUMERICAL METHODS FOR STOCHASTIC MODELS OF POPULATION PROCESSES
WEAK ERROR ANALYSIS OF NUMERICAL METHODS FOR STOCHASTIC MODELS OF POPULATION PROCESSES
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DOI：
10.1137/110849699
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发表时间：
2012-01-01
影响因子：
1.6
通讯作者：
Koyama, Masanori
中科院分区：
文献类型：
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作者：
Anderson, David F.;Koyama, Masanori
最简单和最常见的种群过程的随机模型，包括那些来自生物化学和细胞生物学，是连续时间马尔可夫链。这种模型的模拟通常相对简单，因为有容易实现的方法来生成精确的样本路径。然而，当使用系综平均值来近似期望值时，计算复杂度可能变得过高，因为每个路径的计算数量与过程的跳跃数量线性缩放。当此类方法在计算上变得难以处理时，引入偏差的近似方法可能会变得有利。在本文中，我们提供了一个一般的框架来理解弱误差，或偏见，在当前的设置不同的数值逼近技术引起的。该分析考虑了给定系统内的自然缩放和数值方法的步长。提供的例子来证明的主要分析结果，以及减少计算复杂性所取得的近似方法。
The simplest, and most common, stochastic model for population processes, including those from biochemistry and cell biology, are continuous time Markov chains. Simulation of such models is often relatively straightforward, as there are easily implementable methods for the generation of exact sample paths. However, when using ensemble averages to approximate expected values, the computational complexity can become prohibitive as the number of computations per path scales linearly with the number of jumps of the process. When such methods become computationally intractable, approximate methods, which introduce a bias, can become advantageous. In this paper, we provide a general framework for understanding the weak error, or bias, induced by different numerical approximation techniques in the current setting. The analysis takes into account both the natural scalings within a given system and the step size of the numerical method. Examples are provided to demonstrate the main analytical results as well as the reduction in computational complexity achieved by the approximate methods.