Concentration Inequalities and Martingale Inequalities: A Survey
β Scribed by Chung, Fan; Lu, Linyuan
- Book ID
- 121339123
- Publisher
- A K Peters Ltd
- Year
- 2006
- Tongue
- English
- Weight
- 431 KB
- Volume
- 3
- Category
- Article
- ISSN
- 1542-7951
No coin nor oath required. For personal study only.
π 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 ΒΏ 2, Lesigne and VolnΓ y (Stochastic Process. Appl. 96 (2001) 143) obtained the estimation (S n ΒΏ n) 6 cn -p=2 , which is optimal in a certain sense. In this article, we show that