Concrete Representation of Martingales
Stephen Montgomery-Smith, University of Missouri
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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