By M Csörgö; Barbara Szyszkowicz

ISBN-10: 0444500839

ISBN-13: 9780444500830

ISBN-10: 0585474680

ISBN-13: 9780585474687

ISBN-10: 1281047120

ISBN-13: 9781281047120

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**Additional resources for Asymptotic methods in probability and statistics : a volume in honor of Miklós Csörgö**

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I Primenen. 41 (1996), 520-532. H. Pollard: The completely monotonic character of the Mittag-Leffier function E ~ ( - x ) , Bull. Amer. Math. Soc. 54 (1948), 1115-1116. A. R(~nyi: On mixing sequences of sets, Acta Math. Acad. Sci. Hangar. 9 (1958), 215-228. A. R(~nyi: Foundations of Probability, Holden-Day, San Francisco, 1970. A. R~nyi and P. R6v6sz: On mixing sequences of random variables, Acta Math. Acad. Sci. Hungar. 9 (1958), 389-393. R6v6sz" A limit distribution theorem for sums of dependent random variables, Acta Math.

Let 9V[ - {Mn " n _> 1} be an L ~ process. Following Newman and Wright (1982), we say that :M: is a demimartingale provided that E((Mj+I - M j ) f ( M I , . . , Mj)) >_0 for each integer j >_ 1 and for each coordinatewise-nondecreasing function f " I~J ~ I~, whenever this expectation is defined. Consequently, {Sn "n >_ 0} is an L 2 demimartingale; this will be an important observation in the sequel, when we develop a maximal inequality for this process. 2, respectively; in {}6 we present applications of our theorems to Kesten and Spitzer's random walk in random scenery.

Mj)) >_0 for each integer j >_ 1 and for each coordinatewise-nondecreasing function f " I~J ~ I~, whenever this expectation is defined. Consequently, {Sn "n >_ 0} is an L 2 demimartingale; this will be an important observation in the sequel, when we develop a maximal inequality for this process. 2, respectively; in {}6 we present applications of our theorems to Kesten and Spitzer's random walk in random scenery. 2. PRELIMINARY RESULTS Let H(1) - E(X2), and, for m _>2, let 7n H(m) = E(X12) + 2 E E ( x 1 x j ) .

### Asymptotic methods in probability and statistics : a volume in honor of Miklós Csörgö by M Csörgö; Barbara Szyszkowicz

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