无穷阶马尔可夫链与平衡的渐近满足：在自适应积分法中的应用
Markov Chains of Infinite Order and Asymptotic Satisfaction of Balance: Application to the Adaptive Integration Method
摘要：
自适应蒙特卡罗方法可以被看作是具有无限内存的马尔可夫链的实现。我们推导出一个一般条件的蒙特卡罗方法的收敛性，其历史依赖性包含在模拟的密度分布。在收敛的情况下，我们的结果意味着平衡条件只需要渐近满足。作为一个例子，我们表明，自适应积分方法收敛。
英文摘要：
Adaptive Monte Carlo methods can be viewed as implementations of Markov chains with infinite memory. We derive a general condition for the convergence of a Monte Carlo method whose history dependence is contained within the simulated density distribution. In convergent cases, our result implies that the balance condition need only be satisfied asymptotically. As an example, we show that the adaptive integration method converges.
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