随机游动中首达概率的研究与分析

Research and Analysis on the First Arrival Probability in Random Walk

众所周知,随机游动作为一种特殊的马尔科夫链在诸多领域有着广泛的应用,而研究系统的阈值状态的首达概率则是重中之重。文章首先对对称一维随机游动某状态的首达概率、首达时进行计算分析;然后采用了对递推公式求母函数的方法求解对称一维随机游动的首次返回概率,最后通过蒙特卡洛方法求其首次返回概率的模拟值与理论值对照,通过大样本容量的计算证实理论解的精确性。

As we all know,the random walk is a special Markov chain that has wide applications in many fields,and the research on the first arrival probability of the threshold state of the system is the most important thing.First,the paper calculates and analyzes the first arrival probability and first arrival time of a certain state of a symmetric one-dimensional random walk;then uses the method of finding the generating function of the recurrence formula to solve the first return probability of the symmetric one-dimensional random walk,and finally uses Monte Carlo method compares the simulated value of the probability of its first return with the theoretical value,and confirms the accuracy of the theoretical solution through the calculation of a large sample volume.