Summary
LetR n denote the correlation coefficient of ann-sample of pairs (X i ,Y i ), each distributed as (X, Y). AssumeX andY are independent and in the domain of attraction of the Normal law. It is shown that this entailsXY being in that domain of attraction, and thatd n R n →N(0, 1) in distribution for constantsd n satisfying lim sup(n 1/2/d n )≦1. Examples illustrate details of these limit theorems.
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Hall, P., Seneta, E. Products of independent, normally attracted random variables. Probab. Th. Rel. Fields 78, 135–142 (1988). https://doi.org/10.1007/BF00718041
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DOI: https://doi.org/10.1007/BF00718041
Keywords
- Stochastic Process
- Probability Theory
- Limit Theorem
- Mathematical Biology