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Almost sure convergence and complete convergence for the weighted sums of martingale differences

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Wuhan University Journal of Natural Sciences

Abstract

Let {(D n, FFFn),n/->1} be a sequence of martingale differences and {a ni, 1≤i≤n,n≥1} be an array of real constants. Almost sure convergence for the row sums\(\sum\limits_{i = 1}^n {a_{ni} D_1 } \) are discussed. We also discuss complete convergence for the moving average processes underB-valued martingale differences assumption.

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Authors and Affiliations

  1. College of Mathematical and Computer Sciences, Wuhan University, 430072, Wuhan, China

    Deng Ai-jiao & Liu Jing-jun

Authors
  1. Deng Ai-jiao
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  2. Liu Jing-jun
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Additional information

Foundation item: Supported by the National Natural Science Foundation of China and the Doctoral Programme Foundation of China

Biography: DENG Ai-jiao (1974-), female, Ph.D. candidate. Research interest is in stochastic processes and random fractal.

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Ai-jiao, D., Jing-jun, L. Almost sure convergence and complete convergence for the weighted sums of martingale differences. Wuhan Univ. J. Nat. Sci. 4, 278–284 (1999). https://doi.org/10.1007/BF02842350

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  • DOI: https://doi.org/10.1007/BF02842350

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