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The main goal of this paper is to study an extension of random summations of independent and identically distributed random variables when the number of summands in random summation is a partial sum of n independent, identically distributed, non-negative integer-valued random variables. Some characterizations of random summations are considered. The central limit theorems and weak law of large numbers for extended random summations are established. Some weak limit theorems related to geometric random sums, binomial random sums and negative-binomial random sums are also investigated as asymptotic behaviors of extended random summations.
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참고문헌 (25)
참고문헌 신청
J. Blanchet / 2007 / Uniform renewal theory with applications to expansions of random geometric sums / Adv. in Appl. Probab. 39(4):1070~1097
L. H. Y. Chen / 2011 / Normal approximation by Stein's method, Probability and its Applications (New York) / Springer
L. H. Y. Chen / 2007 / Normal approximation for nonlinear statistics using a concentration inequality approach / Bernoulli 13(2):581~599
R. T. Durrett / 1977 / Weak convergence with random indices / Stochastic Processes Appl 5(3):213~220
W. Feller / 1957 / An Introduction to Probability Theory and its Applications. Vol. I / John Wiley and Sons, Inc.
L. H. Y. Chen / 2011 / Normal approximation by Stein's method, Probability and its Applications (New York) / Springer
L. H. Y. Chen / 2007 / Normal approximation for nonlinear statistics using a concentration inequality approach / Bernoulli 13(2):581~599
R. T. Durrett / 1977 / Weak convergence with random indices / Stochastic Processes Appl 5(3):213~220
W. Feller / 1957 / An Introduction to Probability Theory and its Applications. Vol. I / John Wiley and Sons, Inc.
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