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Concrete Representation of Martingales
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Stephen Montgomery-Smith, University of Missouri
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Abstract
Let (fn) be a mean zero vector valued martingale sequence.
Then there exist vector valued functions (dn) from [0,1]n
such that
int01 dn(x1,...,xn)
dxn = 0
for almost all x1,...,xn-1, and such that the law of
(fn) is the same
as the law of
( sumk=1n
dk(x1,...,xk) ) .
Similar results for tangent sequences and sequences satisfying condition
(C.I.) are presented.
We also present a weaker version of a result of McConnell that provides a
Skorohod like representation for vector valued martingales.
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Full text: PDF
Pages: 1-15
Published on: December 2, 1998
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Bibliography
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Math Review link
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T.R. McConnell, A Skorohod-like representation in infinite
dimensions, Probability in Banach spaces, V (Medford, Mass.,
1984), 359-368,
Lecture Notes in Math., 1153, Springer, Berlin-New York, 1985.
Math Review link
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T.R. McConnell, Decoupling and stochastic integration in
UMD Banach spaces, Probab. Math. Statist. 10, (1989),
283--295.
Math Review link
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Electronic Journal of Probability. ISSN: 1083-6489 |
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Context