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_{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
- Publication:
-
arXiv Mathematics e-prints
- Pub Date:
- June 1998
- DOI:
- 10.48550/arXiv.math/9806022
- arXiv:
- arXiv:math/9806022
- Bibcode:
- 1998math......6022M
- Keywords:
-
- Probability;
- 60G42 60H05
- E-Print:
- Also available at http://math.missouri.edu/~stephen/preprints