1. Introduction. Let (X,) be a sequence of real valued independent and identically distributed random variables (r. v.) with espactation 0 and finite second moment 02. Further, let ( N n ) be a sequence of random integers satisfying N,/n -. t where z is a positive r.v. Then the celebrated result of
β¦ LIBER β¦
Convergence inr-mean of normalized partial sums in a separable Banach space
β Scribed by A. I. Dale
- Publisher
- Springer
- Year
- 1977
- Tongue
- English
- Weight
- 193 KB
- Volume
- 24
- Category
- Article
- ISSN
- 0026-1335
No coin nor oath required. For personal study only.
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For weighted sums of the form Sn = Ejknl anj (Vnj--Cnj) where {anj, 1 <<.j<~kn < oo, n~> 1} are constants, {V~j, 1 <~j<~k~, n>~l} are random elements in a real separable martingale type p Banach space, and {cnj, 1 <<.j<~kn, n>>-1} are suitable conditional expectations, a mean convergence theorem and