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A Weak Convergence Theorem for Functionals of Sums of Martingale Differences

✍ Scribed by Z. Rychlik; I. Szyszkowski

Publisher
John Wiley and Sons
Year
1987
Tongue
English
Weight
195 KB
Volume
130
Category
Article
ISSN
0025-584X

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✦ Synopsis

For each n, let ( S n k ) , 1 S k s k,, be a mean zero square -integrable martingale adapted to increasing a-fields ($nk), O s k s h n , and let ( b n k ) , OSkaE,, be a system of random variables such that bno=O -=bnl-=... -= bnkn= 1 and such that bnk is Snn,k-l measurable for each k. We present sufficient conditions under which 2 f,(b,i, S, J (Sn,i+l -&i) Gd f ( t , F ( t ) ) clIB(t) as n--, where (W(t) : O s t s l ) is a standard WIENER process.

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