Concentration inequalities for semi-bounded martingales

Yu Miao

ESAIM: Probability and Statistics (2008)

  • Volume: 12, page 51-57
  • ISSN: 1292-8100

Abstract

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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.

How to cite

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Miao, Yu. "Concentration inequalities for semi-bounded martingales." ESAIM: Probability and Statistics 12 (2008): 51-57. <http://eudml.org/doc/244815>.

@article{Miao2008,
abstract = {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.},
author = {Miao, Yu},
journal = {ESAIM: Probability and Statistics},
keywords = {decoupling; exponential inequalities; martingale; conditionally symmetric variables},
language = {eng},
pages = {51-57},
publisher = {EDP-Sciences},
title = {Concentration inequalities for semi-bounded martingales},
url = {http://eudml.org/doc/244815},
volume = {12},
year = {2008},
}

TY - JOUR
AU - Miao, Yu
TI - Concentration inequalities for semi-bounded martingales
JO - ESAIM: Probability and Statistics
PY - 2008
PB - EDP-Sciences
VL - 12
SP - 51
EP - 57
AB - 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.
LA - eng
KW - decoupling; exponential inequalities; martingale; conditionally symmetric variables
UR - http://eudml.org/doc/244815
ER -

References

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  1. [1] A. Maurer, Abound on the deviation probability for sums of non-negative random variables. J. Inequa. Pure Appl. Math. 4 (2003) Article 15. Zbl1021.60036MR1965995
  2. [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. Zbl0796.60020MR1276997
  3. [3] V.H. De La Peña, A general class of exponential inequalities for martingales and ratios. Ann. Probab. 27 (1999) 537–564. Zbl0942.60004MR1681153
  4. [4] A. Jakubowski, Principle of conditioning in limit theorems for sums of random varibles. Ann. Probab. 14 (1986) 902–915. Zbl0593.60031MR841592
  5. [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. Zbl0693.60033MR1035249
  6. [6] S. Kwapień and W.A. Woyczyński, Random series and Stochastic Integrals: Single and Multiple. Birkhäuser, Boston (1992). Zbl0751.60035MR1167198
  7. [7] I. Pinelis, Optimum bounds for the distributions of martingales in Banach space. Ann. Probab. 22 (1994) 1679–1706. Zbl0836.60015MR1331198
  8. [8] G.L. Wise and E.B. Hall, Counterexamples in probability and real analysis. Oxford Univ. Press, New York.(1993). Zbl0827.26001MR1256489

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