Stephen Montgomery-Smith, Concrete representation of martingales. Electronic J. Probability, 3, (1998), Paper 15. 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 \(\int_0^1 d_n(x_1,\dots,x_n)\,dx_n = 0\) for almost all \(x_1,\dots,x_{n-1}\), and such that the law of \((f_n)\) is the same as the law of \((\sum_{k=1}^n d_k(x_1,\dots,x_k))\). 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. (tex, dvi, ps, pdf).


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