Article contents
Some inequalities for martingales and applications to the study of L1
Published online by Cambridge University Press: 24 October 2008
Abstract
We obtain here estimates for the expectation of a restricted quadratic variation of L1 bounded (weak) martingales and positive submartingales, and for related functionals. These inequalities are then used to give a quantitative version of a recent result of D. J. Aldous and D. H. Fremlin concerning the L1 norms of expansions with respect to uniformly integrable L1-normalized martingale difference sequences. Another application relates precisely the degree of norm divergence of an L1-bounded martingale to the degree of non-uniform integrability of that martingale. A partial analogue of this result is proved for certain vector valued martingales with values in L1 which are related to the Radon–Nikodým property.
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 89 , Issue 1 , January 1981 , pp. 135 - 148
- Copyright
- Copyright © Cambridge Philosophical Society 1981
References
- 1
- Cited by