Distribution and moment convergence of martingales |
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| Authors: | H Teicher |
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| Institution: | (1) Department of Statistics, Hill Center for Mathematical Sciences, Rutgers University, 08903 New Brunswick, NJ, USA |
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| Abstract: | Summary If
where {X
n j
,ℱ
n j
1≦j≦m
n
↑∞, n≧1} is a martingale difference array, conditions are given for the distribution and moment convergence of S
n,k
to the distribution and moments of
where H
k
is the Hermite polynomial of degree k and Z is a standard normal variable. This is intimately related to an identity (*) for multiple Wiener integrals. Under alternative
conditions, similar results hold for S
n, k
/U
n
k
and S
n, k
/V
n
k
where
and V
n
2
V
n
2
is the conditional variance.
Research supported by the National Science Foundation under Grant DMS-8601346 |
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| Keywords: | |
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