关于可列马氏链状态出现频率延迟平均的强大数定律

对于齐次马氏链由有限状态推广到可列的情形,由于可列和与极限运算不能交换,与文中证明方法与有限情形不同.利用了二元函数延迟平均的强极限定理和条件期望的平滑性,研究可列齐次马氏链状态出现频率延迟平均的强大数定律.

The Strong Law of Large Numbers for the Delay Mean of Frequencies of Occurrence of Countable States for Homogeneous Markov Chains

Homogeneous Markov chains can be extended from finite states to countable states.However, as the countable sum and limit operation cannot be exchanged, the method is different from the finite state for Markov chains.The strong limit theorem for the delay mean of function of two variables and the smoothness of conditional expectation were applied to study the strong law of large numbers for the delay mean of frequencies of occurrence for countable states of homogeneous Markov chains.