Exact simulation of continuous time Markov jump processes with anticorrelated variance reduced Monte Carlo estimation
Exact simulation of continuous time Markov jump processes with anticorrelated variance reduced Monte Carlo estimation
复制标题
使用反相关方差减少蒙特卡罗估计精确模拟连续时间马尔可夫跳跃过程
DOI：
10.1109/cdc.2014.7039916
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
G. Dullerud
中科院分区：
文献类型：
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作者：
Peter A. Maginnis;Matthew West;G. Dullerud
我们提供了一个精确的，连续的时间扩展到以前的工作，在反相关的随机过程模拟是在一个近似的，离散的时间设置。这些方法减小了马尔可夫跳变过程系统的连续时间蒙特卡罗方差。我们严格构造了对偶泊松过程，并解析证明了对之间的负相关关系。然后，我们展示了这些反相关泊松过程如何通过随机时间变化表示来驱动马尔可夫跳跃过程。最后，给出了跳跃过程中方差减小的充分条件，并给出了一个简单的例子。
We provide an exact, continuous time extension to previous work in anticorrelated stochastic process simulation that was performed in an approximate, discrete time setting. These methods reduce the variance of continuous time Monte Carlo for Markov jump process systems. We rigorously construct antithetic Poisson processes and analytically prove the negative correlation between pairs. We then show how these anticorrelated Poisson processes can be used to drive Markov jump processes via a random time change representation. Finally, we provide a sufficient condition for variance reduction in the jump process context as well as demonstrate a simple example.