Some deviation inequalities
✍ Scribed by B. Maurey
- Publisher
- Springer
- Year
- 1991
- Tongue
- English
- Weight
- 387 KB
- Volume
- 1
- Category
- Article
- ISSN
- 1016-443X
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
Using martingale techniques we will prove several deviation inequalities for diffusion processes in a compact Riemannian manifold and Le vy processes in euclidean space. We also deduce deviation inequalities from Poincare type inequalities in the abstract setting of Dirichlet forms. We thus obtain,
Let (X i ) be a martingale di erence sequence and let S n = n i=1 X i . Suppose (X i ) is bounded in L p . In the case p ¿ 2, Lesigne and Volnà y (Stochastic Process. Appl. 96 (2001) 143) obtained the estimation (S n ¿ n) 6 cn -p=2 , which is optimal in a certain sense. In this article, we show that
## Abstract In the present work are proved linear generalizations of the classical Gronwall‐Bellman's integral inequality on partially continuous functions with a constant deviation.