Zentralblatt MATH
Publications of (and about) Paul Erdös
Zbl.No: 042.37601
Autor: Chung, Kai Lai; Erdös, Pál
Title: Probability limit theorems assuming only the first moment. I. (In English)
Source: Mem. Am. Math. Soc. 6 (Four papers on probability), 19 p. (1951).
Review: Let Xi (i = 1,2,...) be independent, identically distributed random variables which assume only integer values and write P(X = k) = pk. The authors consider the following assumptions: \TagsOnLeft sumk = -oooo | k| pk < oo sumk = -oooo k pk = 0 (2)sumk = 0oo k pk = -sumk = -oo0 k pk = oo. (1) They derive the following main results: I. Under either (1) or 2) limn = oo {P { Sn = a } \over P{ Sn = a' }} = 1 where Sn = X1+X2+···+Xn and a and a' are arbitrary integers. II. Under (1) P \left { limn = oo {sumk = 1n Yk \over sumk = 1n Y'k} = 1 \right } = 1 where Yk = 1 if Sk = a and = 0 if Sk \ne a, and similarly Yk' for a'.
Reviewer: Stefan Vajda
Classif.: * 60F05 Weak limit theorems
Index Words: probability theory
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