In this paper, we apply the technique of decoupling to obtain some exponential inequalities for semi-bounded martingale, which extend the results of de la Peña, Ann. probab. 27 (1999) 537-564.
Mots clés : decoupling, exponential inequalities, martingale, conditionally symmetric variables
@article{PS_2008__12__51_0, author = {Miao, Yu}, title = {Concentration inequalities for semi-bounded martingales}, journal = {ESAIM: Probability and Statistics}, pages = {51--57}, publisher = {EDP-Sciences}, volume = {12}, year = {2008}, doi = {10.1051/ps:2007033}, mrnumber = {2367993}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/ps:2007033/} }
Miao, Yu. Concentration inequalities for semi-bounded martingales. ESAIM: Probability and Statistics, Tome 12 (2008), pp. 51-57. doi : 10.1051/ps:2007033. http://archive.numdam.org/articles/10.1051/ps:2007033/
[1] Abound on the deviation probability for sums of non-negative random variables. J. Inequa. Pure Appl. Math. 4 (2003) Article 15. | MR | Zbl
,[2] A bound on the moment generating function of a sum of dependent variables with an application to simple random sampling without replacement. Ann. Inst. H. Poincaré Probab. Staticst. 30 (1994) 197-211. | Numdam | MR | Zbl
,[3] A general class of exponential inequalities for martingales and ratios. Ann. Probab. 27 (1999) 537-564. | MR | Zbl
,[4] Principle of conditioning in limit theorems for sums of random varibles. Ann. Probab. 14 (1986) 902-915. | MR | Zbl
,[5] Tangent sequences of random variables: basic inequalities and their applications, in Proceeding of Conference on Almost Everywhere Convergence in Probability and Ergodic Theory, G.A. Edgar and L. Sucheston Eds., Academic Press, New York (1989) 237-265. | MR | Zbl
and ,[6] Random series and Stochastic Integrals: Single and Multiple. Birkhäuser, Boston (1992). | MR | Zbl
and ,[7] Optimum bounds for the distributions of martingales in Banach space. Ann. Probab. 22 (1994) 1679-1706. | MR | Zbl
,[8] Counterexamples in probability and real analysis. Oxford Univ. Press, New York.(1993). | MR | Zbl
and ,Cité par Sources :