A local convergence theorem for partial sums of stochastic adapted sequences |
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| Authors: | Weiguo Yang Zhongxing Ye Wen Liu |
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| Affiliation: | (1) Faculty of Science, Jiangsu University, Zhenjiang, 212013, P.R. China;(2) Department of Mathematics, Shanghai Jiaotong University, Shanghai, 200240, P.R. China;(3) Department of Mathematics, Hebei University of Technology, Tianjin, 300130, P.R. China |
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| Abstract: | In this paper we establish a new local convergence theorem for partial sums of arbitrary stochastic adapted sequences. As
corollaries, we generalize some recently obtained results and prove a limit theorem for the entropy density of an arbitrary
information source, which is an extension of case of nonhomogeneous Markov chains. |
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| Keywords: | local convergence theorem stochastic adapted sequence martingale |
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