一类特殊马氏链首达问题的巧解及其计算机模拟

Ingenious solution to first arrival time of a class of Markov chain and it's data simulation

研究了一类特殊马氏链——立方体、锥体上等有逗留与无逗留等概率的随机游走的相关性质,我们得到了其平稳分布、平均回返时、首次回返时等一系列结论。讨论在正四面锥上的随机游走平稳分布以及n面锥的极限状况。特别地,对一类特殊马氏链巧妙利用状态空间的对称性得到先于状态a首中状态b的概率。

This paper studies a special class of Markov Chain. We obtain the related properties of Random Walk, staying in or not staying, with equal probability on cube etc. We acquire a series of conclusions such as stationary distribution, the average return time and first return time. In addition to give strict proof, we also use Data Simulation which is very similar to real val- ue. Explicitly, that exists stationary uniform distribution on Regular tetrahedr, and we get limit result of it. Particularly, using the symmetry of state space, the probability of arriving state B before state A can be smartly gotten, what is more, we discusses the application of the method.