A Hoeffding-Azuma Type Inequality for Random Processes

Hasanov, Mahir

doi:10.28924/2291-8639-21-2023-104

Research Article

A Hoeffding-Azuma Type Inequality for Random Processes

Mahir Hasanov¹

a:1:{s:5:"en_US";s:18:"Beykent University";}

Abstract

The subject of this paper is a Hoeffding-Azuma type estimation for the difference between an adapted random process and its conditional expectation given a related filtration.

How to Cite

M. Hasanov, A Hoeffding-Azuma Type Inequality for Random Processes, Int. J. Anal. Appl. 21 (2023), 104. https://doi.org/10.28924/2291-8639-21-2023-104

BibTeX

@article{Hasanov2023,
  author  = {Hasanov, Mahir},
  title   = {A Hoeffding-Azuma Type Inequality for Random Processes},
  journal = {Int. J. Anal. Appl.},
  volume  = {21},
  year    = {2023},
  pages   = {104},
  doi     = {10.28924/2291-8639-21-2023-104}
}

References

[1] K.B. Athreya, S.N. Lahiri, Measure theory and probability theory, Springer New York, 2006. https://doi.org/10.1007/978-0-387-35434-7.
[2] V. Bentkus, On Hoeffding’s inequalities, Ann. Probab. 32 (2004), 1650–1673. https://doi.org/10.1214/009117904000000360.
[3] V. Bentkus, An extension of the Hoeffding inequality to unbounded random variables, Lith Math. J. 48 (2008), 137–157. https://doi.org/10.1007/s10986-008-9007-7.
[4] P.W. Glynn, D. Ormoneit, Hoeffding’s inequality for uniformly ergodic Markov chains, Stat. Probab. Lett. 56 (2002), 143–146. https://doi.org/10.1016/s0167-7152(01)00158-4.
[5] G.R. Grimmett, D.R. Stirzaker, Probability and random processes, Oxford University Press, Oxford, New York, 2004.
[6] W. Hoeffding, Probability inequalities for sums of bounded random variables, J. Amer. Stat. Assoc. 58 (1963), 13–30. https://doi.org/10.1080/01621459.1963.10500830.
[7] I. Pinelis, On the Bennett-Hoeffding inequality, Ann. Inst. H. Poinc. Probab. Stat. 50 (2014), 123–145. https://doi.org/10.1214/12-aihp495.
[8] M. Talagrand, The missing factor in Hoeffding’s inequalities, Ann. Inst. Henri Poinc. 31 (1995), 689–702.
[9] T. Tao, Topics in Random Matrix Theory, Graduate Studies in Mathematics, Vol. 132, American Mathematical Society, 2012.
[10] S.A. Van De Geer, On Hoeffding’s inequality for dependent random variables, in: H. Dehling, T. Mikosch, M. Sørensen (Eds.), Empirical Process Techniques for Dependent Data, Birkhäuser, Boston, 2002: pp. 161–169. https://doi.org/10.1007/978-1-4612-0099-4_4.