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On the weak law for randomly indexed partial sums for arrays of random elements in martingale type p Banach spaces

✍ Scribed by Dug Hun Hong; Manuel Ordóñez Cabrera; Soo Hak Sung; Andrei I. Volodin

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
104 KB
Volume
46
Category
Article
ISSN
0167-7152

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✦ Synopsis

For weighted randomly indexed sums of the form Nn j = 1 anj(Vnj -cnj) where {anj; j¿1; n¿1} are constants, {Vnj; j¿1; n¿1} are random elements in a real separable martingale type p Banach space, {Nn; n¿1} are positive integer-valued random variables, and {cnj; j¿1; n¿1} are suitable conditional expectations, a general weak law of large numbers is established. No conditions are imposed on the joint distributions of the {Vnj; j¿1; n¿1}. Also, no conditions are imposed on the joint distributions of {Nn; n¿1}. Moreover, no conditions are imposed on the joint distributions of {Nn; n¿1}. Moreover, no conditions are imposed on the joint distribution of the sequence {Vnj; j¿1; n¿1} and the sequence {Nn; n¿1}. The weak law is proved under a Ces aro type condition. The sharpness of the results is illustrated by an example. The current work extends that of Gut

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