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Finiteness of moments of randomly stopped sums of i.i.d. random variables

✍ Scribed by Saeed Ghahramani; Ronald W. Wolff

Publisher
Elsevier Science
Year
1989
Tongue
English
Weight
135 KB
Volume
8
Category
Article
ISSN
0167-7152

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The corresponding moderate deviation principle follows. The Central Limit theorem has been recently obtained by Pang, Lin and Hwang [T.X. Pang, Z.Y. Lin, K.S. Hwang, Asymptotics for self-normalized random products of sums of i.i.d. random variables, J. Math. Anal. Appl. 334 (2007) 1246-1259].

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For S= x i ! i , where (! i ) is a sequence of independent, symmetric random variables and (x i ) is a sequence of vectors in a normed space we give two methods of proving inequalities (E &S& p ) 1Γ‚p C p, q (E &S& q ) 1Γ‚q with the constants C p, q independent of the sequence (x i ). The methods depe