Central Limit Theorem for dependent random variables

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I am looking for a Central Limit Theorem for dependent random variables that is guaranteed by zero correlations between
all random variables plus some testable addition condition or conditions. I understand that uncorrelatedness by itself does not
guarantee a CLT (stated in Varadhan's book Probability Theory). A reference would also be greatly appreciated. In my problem,
the variance of each random variable is finite and nonzero, but tends to infinity as the number of random variables n tends to infinity.










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    I am looking for a Central Limit Theorem for dependent random variables that is guaranteed by zero correlations between
    all random variables plus some testable addition condition or conditions. I understand that uncorrelatedness by itself does not
    guarantee a CLT (stated in Varadhan's book Probability Theory). A reference would also be greatly appreciated. In my problem,
    the variance of each random variable is finite and nonzero, but tends to infinity as the number of random variables n tends to infinity.










    share|cite|improve this question























      up vote
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      down vote

      favorite









      up vote
      0
      down vote

      favorite











      I am looking for a Central Limit Theorem for dependent random variables that is guaranteed by zero correlations between
      all random variables plus some testable addition condition or conditions. I understand that uncorrelatedness by itself does not
      guarantee a CLT (stated in Varadhan's book Probability Theory). A reference would also be greatly appreciated. In my problem,
      the variance of each random variable is finite and nonzero, but tends to infinity as the number of random variables n tends to infinity.










      share|cite|improve this question













      I am looking for a Central Limit Theorem for dependent random variables that is guaranteed by zero correlations between
      all random variables plus some testable addition condition or conditions. I understand that uncorrelatedness by itself does not
      guarantee a CLT (stated in Varadhan's book Probability Theory). A reference would also be greatly appreciated. In my problem,
      the variance of each random variable is finite and nonzero, but tends to infinity as the number of random variables n tends to infinity.







      central-limit-theorem






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      asked Sep 7 at 9:34









      Mostafa Naseri

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