By M Csörgö; Barbara Szyszkowicz
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Extra info for Asymptotic methods in probability and statistics : a volume in honor of Miklós Csörgö
Gebiete 1, 389-393. CsSrgS, M. and S. CsSrg5 (1973), On weak convergence of randomly selected partial sums, Acta Sci. Math. Szeged 34, 53-60. CsSrgS, M. and R. Fischler (1970), Departure from independence: the strong law, standard and random - sum central limit theorems, Acta Math. Acad. Sci. Hung. 21, 105-114. CsSrgS, M. and R. Fischler (1973), Some examples and results in the theory of mixing and random - sum central limit theorem, Period. Math. Hungar. 3, 41-57. CsSrgS, M. and Z. Rychlik (1980), Weak convergence of sequences of random elements with random indices, Proc.
We can partially order the members of HI accordingly: 32 given p, q E HI, we will say that p is less than q (written p < q) provided that max p < min q. In this notation, we say that II is quasi-associated provided that C o v ( f ( U " p), g(U; q)) > 0 for all p, q E HI with p < q and for all coordinatewise-nondecreasing, measurable functions f 9 ll~lpl ~ ll( and g 9 Rlql --. R, whenever the covariance is defined. Observe that p < q implies p N q - 0; thus, when the index set is ordered, quasi-association is the weakest form of association.
Kesten: A Tauberian theorem for random walk, Israel J. Math. 6 (1968), 279-294. H. Kesten: A sharper form of the Doeblin- L~vy - Kolmogorov- Rogozin inequality for concentration functions, Math. Scan& 25 (1969), 133-144. P. Kowalski and Z. Rychlik: Limit theorems for maximal random sums, In this volume. M. Kruglov and Bo Zhang: Limit theorems for maximal random sums [in Russian], Teor. Veroyatnost. i Primenen. 41 (1996), 520-532. H. Pollard: The completely monotonic character of the Mittag-Leffier function E ~ ( - x ) , Bull.