Using Simulation to Estimate First Passage Distribution
针对离散时间马尔可夫过程，提出基于“观测风险”的估计量来改进蒙特卡洛估计，用于估计过程首次进入某状态集的转移次数及首次到达状态的分布，并扩展至连续时间。
Consider a discrete time Markov process {X n , n > 0}. For a given subset 𝒜 of the state space, consider the problem of using simulation to estimate the number of transitions it takes the process to enter 𝒜. Using estimators based on the “observed hazard,” we are able to improve on the usual Monte Carlo estimator. We also consider the problem of estimating the distribution of the first state in, 𝒜 to be reached, and then extend our results to continuous time.