منابع مشابه
A Note on the Strong Law of Large Numbers
Petrov (1996) proved the connection between general moment conditions and the applicability of the strong law of large numbers to a sequence of pairwise independent and identically distributed random variables. This note examines this connection to a sequence of pairwise negative quadrant dependent (NQD) and identically distributed random variables. As a consequence of the main theorem ...
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The Loeb space construction in nonstandard analysis is applied to the theory of processes to reveal basic phenomena which cannot be treated using classical methods. An asymptotic interpretation of results established here shows that for a triangular array (or a sequence) of random variables, asymptotic uncorrelatedness or asymptotic pairwise independence is necessary and sufficient for the vali...
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Abstract. Let X1, X2, . . . denote i.i.d. random bits, each taking the values 1 and 0 with respective probabilities p and 1 − p. A well-known theorem of Erdős and Rényi (1970) describes the length of the longest contiguous stretch, or “run,” of ones in X1, . . . , Xn for large values of n. Benjamini, Häggström, Peres, and Steif (2003, Theorem 1.4) demonstrated the existence of unusual times, pr...
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We study the following problem: If ξ1, ξ2, . . . are fuzzy numbers with modal values M1, M2, . . . , then what is the strongest t-norm for which lim n→∞ Nes ( mn − ≤ ξ1 + · · ·+ ξn n ≤ mn + ) = 1, for any > 0, where mn = M1 + · · ·+Mn n , the arithmetic mean ξ1 + · · ·+ ξn n is defined via sup-t-norm convolution and Nes denotes necessity.
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ژورنال
عنوان ژورنال: The Annals of Probability
سال: 1980
ISSN: 0091-1798
DOI: 10.1214/aop/1176994830