Concrete representation of martingales
Abstract
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_{n1}, 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
 Publication:

arXiv Mathematics eprints
 Pub Date:
 June 1998
 DOI:
 10.48550/arXiv.math/9806022
 arXiv:
 arXiv:math/9806022
 Bibcode:
 1998math......6022M
 Keywords:

 Probability;
 60G42 60H05
 EPrint:
 Also available at http://math.missouri.edu/~stephen/preprints