Concentration inequalities for semi-bounded martingales
ESAIM: Probability and Statistics, Tome 12 (2008), pp. 51-57.

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.

DOI : https://doi.org/10.1051/ps:2007033
Classification : 60E15,  60G42
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://www.numdam.org/articles/10.1051/ps:2007033/}
}
TY  - JOUR
AU  - Miao, Yu
TI  - Concentration inequalities for semi-bounded martingales
JO  - ESAIM: Probability and Statistics
PY  - 2008
DA  - 2008///
SP  - 51
EP  - 57
VL  - 12
PB  - EDP-Sciences
UR  - http://www.numdam.org/articles/10.1051/ps:2007033/
UR  - https://www.ams.org/mathscinet-getitem?mr=2367993
UR  - https://doi.org/10.1051/ps:2007033
DO  - 10.1051/ps:2007033
LA  - en
ID  - PS_2008__12__51_0
ER  - 
Miao, Yu. Concentration inequalities for semi-bounded martingales. ESAIM: Probability and Statistics, Tome 12 (2008), pp. 51-57. doi : 10.1051/ps:2007033. http://www.numdam.org/articles/10.1051/ps:2007033/

[1] A. Maurer, Abound on the deviation probability for sums of non-negative random variables. J. Inequa. Pure Appl. Math. 4 (2003) Article 15. | MR 1965995 | Zbl 1021.60036

[2] V.H. De La Peña, 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 1276997 | Zbl 0796.60020

[3] V.H. De La Peña, A general class of exponential inequalities for martingales and ratios. Ann. Probab. 27 (1999) 537-564. | MR 1681153 | Zbl 0942.60004

[4] A. Jakubowski, Principle of conditioning in limit theorems for sums of random varibles. Ann. Probab. 14 (1986) 902-915. | MR 841592 | Zbl 0593.60031

[5] S. Kwapień and W.A. Woyczyński, 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 1035249 | Zbl 0693.60033

[6] S. Kwapień and W.A. Woyczyński, Random series and Stochastic Integrals: Single and Multiple. Birkhäuser, Boston (1992). | MR 1167198 | Zbl 0751.60035

[7] I. Pinelis, Optimum bounds for the distributions of martingales in Banach space. Ann. Probab. 22 (1994) 1679-1706. | MR 1331198 | Zbl 0836.60015

[8] G.L. Wise and E.B. Hall, Counterexamples in probability and real analysis. Oxford Univ. Press, New York.(1993). | MR 1256489 | Zbl 0827.26001

Cité par Sources :