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Database: ingentaconnect
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TY - ABST
AU - Mynbaev, K.T.
TI - **L**_{p}-Approximable Sequences of Vectors and Limit Distribution of Quadratic Forms of Random Variables
JO - Advances in Applied Mathematics
PY - 2001-05-01T00:00:00///
VL - 26
IS - 4
SP - 302
EP - 329
KW - quadratic forms of random variables
KW - linear operators in Lp spaces
KW - central limit theorem
N2 - The properties of **L**_{2}-approximable sequences established here form a complete toolkit for statistical results concerning weighted sums of random variables, where the weights are nonstochastic sequences approximated in some sense by square-integrable functions and the random variables are “two-wing” averages of martingale differences. The results constitute the first significant advancement in the theory of **L**_{2}-approximable sequences since 1976 when Moussatat introduced a narrower notion of **L**_{2}-generated sequences. The method relies on a study of certain linear operators in the spaces **L**_{p} and **l**_{p}. A criterion of **L**_{p}-approximability is given. The results are new even when the weight generating function is identically 1. A central limit theorem for quadratic forms of random variables illustrates the method.
UR - http://www.ingentaconnect.com/content/ap/am/2001/00000026/00000004/art00723
ER -