Rsearch On Some Problems Of Probability Limit Theory For Random Variable Sequences

Probability limit theory is an important research field of probability and mathematicalstatistics. Moreover, random variables sequence limit properties is one of the very impor-tant problem in probability limit theory, which has extremely profound applications in areassuch as time series analysis, information theory, stochastic decision-making, investment,actuarial, finance analysis, statistics, large sample theory. In this thesis, we further studyseveral issues of random variables sequence limit theory.The full arrangement of this paper is given as follows:In chapter two, we achieve countable non-homogeneous markov chains coefficient ofstrong limit theorem by convergence theorem of martingale difference sequence.In chapter three, we prove chung type law of large numbers for A triangular array ofNA random variables under the condition of all kinds of moment.In chapter four, the almost everywhere convergence martingale has been constructedby the truncation method, besides, we obtain the local convergence and strong law of largenumbers of arbitrary random sequence by martingale method combined with analysis me-thod.In chapter five, we directly structure sliding likelihood ratio and prove almost every-where convergence of random sequence by Borel-Cantelli lemma.In chapter six, we firstly introduce the concept of non-homogeneous markov chains inrandom transition probability of the random transformation and construct the new probabil-ity measure, then get finite markov chains in random transition probability random har-monic average and some strong limit theorem of random geometric average.