Concrete representation of martingales

Details Concrete representation of martingales Concrete representation of martingales

1998-06-05

arxiv.org/abs/math/9806022v2

Electronic J. Probability, 3, (1998), Paper 15

Mathematics

Probability

Also available at http://math.missouri.edu/~stephen/preprints

Scientific paper

Let (f_n) be a mean zero vector valued martingale sequence. Then there exist vector valued functions (d_n) from [0,1]^n such that int_0^1 d_n(x_1,...,x_n) dx_n = 0 for almost all x_1,...,x_{n-1}, and such that the law of (f_n) is the same as the law of (sum_{k=1}^n d_k(x_1,...,x_k)) . 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. This paper may be found at http://math.missouri.edu/~stephen/preprints

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