在有限的马尔科夫链中稳定且可扩展的计算状态访问概率
Daniel J Sharpe1, David J Wales1
1Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom.
The Journal of chemical physics
|June 5, 2023
概括
我们开发了一个重新规范化算法来计算在有限的马尔科夫链中两个状态之间的过渡期间访问特定状态的概率. 这种方法在数值上稳定且高效,避免了大型矩阵存储.
科学领域:
- 计算数学 计算数学 计算数学
- 可能性理论概率理论.
- 算法开发 算法开发
背景情况:
- 有限马尔科夫链被广泛用于模拟具有离散状态和过渡的系统.
- 计算状态之间的通道概率对于理解系统动态至关重要.
- 现有的方法可能面临数值不稳定性或需要大量的计算资源.
研究的目的:
- 介绍一种新的算法,用于计算有限马尔科夫链中的状态访问概率.
- 解决现有方法在数值稳定性和内存要求方面的局限性.
- 为分析第一通道和过渡路径提供强大的计算工具.
主要方法:
- 该研究采用基于重新规范化的算法.
- 算法计算访问特定状态或状态集的概率.
- 它专注于有限的马尔科夫链中两个定义的终点状态之间的路径.
主要成果:
- 拟议的算法在数值上是稳定的.
- 它有效地计算所需的概率,而不需要密集存储过渡矩阵.
- 证明了对第一通道和过渡路径分析的适用性.
结论:
- 重规范化算法为计算有限马尔科夫链中的状态访问概率提供了一种稳定高效的方法.
- 这种方法推进了对随机过程中路径依赖性质的分析.
- 该算法的效率使其适用于大规模或计算密集型应用程序.
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