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  1. Weak and strong law of large numbers for strictly stationary Banach-valued random fields[pdf]
  2. Deviation inequality for Banach-valued orthomartingales[pdf]
  3. Functional central limit theorem and Marcinkiewicz strong law of large numbers for Hilbert-valued U-statistics of absolutely regular data[pdf]
  4. Some notes on ergodic theorem for U-statistics of order m for stationary and not necessarily ergodic sequences[pdf]


Title Co-authors Journal Volume Arxiv/HAL DOI
21. U-statistics of local sample moments under weak dependence Herold Dehling et Sara Schmidt ALEA Lat. Am. J. Probab. Math. Stat. 20 (2023), no. 2, 1511–1535. [pdf]
20. Some remarks on the ergodic theorem for 𝑈 -statistics Herold Dehling et Dalibor Volný Comptes Rendus Mathématique 361 (2023), 1511–1519. PDF
19. An exponential inequality for orthomartingale differences random fields and some applications - Annales Henri Lebesgue 6 (2023) 575-594 [Arxiv] [DOI]
18. Change-Point Tests for the Tail Parameter of Long Memory Stochastic Volatility Time Series Annika Betken et Rafal Kulik Statistica Sinica (2023), no. 3, 2017–2039. [Arxiv] [DOI]
17. Bound on the maximal function associated to the law of the iterated logarithms for Bernoulli random fields, - Stochastics 94 (2022), no. 2, 248–276. [Arxiv] [DOI]
16. An Exponential Inequality for \(U\)-Statistics of I.I.D. Data, - Theory of Probability & Its Applications 2021, Vol. 66, No. 3 : pp. 408-429 [Arxiv] [DOI]
15. Convergence of the empirical two-sample \(U\)-statistics with \(\beta\)-mixing data. Herold Dehling et Olimjon Sharipov Acta Math. Hungar. 164 (2021), no. 2, 377--412. [Arxiv] [DOI]
14. Limit theorems for \(U\)-statistics of Bernoulli data. - ALEA Lat. Am. J. Probab. Math. Stat. 18 (2021), no. 1, 793--828 [Arxiv] [DOI]
13. Maximal function associated to the bounded law of the iterated logarithms via orthomartingale approximation. - J. Math. Anal. Appl. 496 (2021), no. 1, Paper No. 124792, 25 pp [Arxiv] [DOI]
12. Deviation inequalities for Banach space valued martingales differences sequences and random fields. - ESAIM Probab. 23 (2019), 922--946. [Arxiv] [DOI]
11. Convergence rates in the central limit theorem for weighted sums of Bernoulli random fields - Mod. Stoch. Theory Appl. 6 (2019), no. 2, 251–267. [HAL] [DOI]
10. Invariance principle via orthomartingale approximation - Stoch. Dyn. 18 (2018), no. 6, 1850043, 29 pp. [HAL] [DOI]
9. Hölderian weak invariance principle under Maxwell and Woodroofe condition - Brazilian Journal of Probability and Statistics 32 (2018), no. 1, 172–187. [HAL] [DOI]
8. Weak invariance principle in Besov spaces for stationary martingale differences Alfredas Račkauskas Lith. Math. J. 57 (2017), no. 4, 441--467. [HAL] [DOI]
7. Holderian weak invariance principle for stationary mixing sequences - Journal of Theoretical Probability 30 (2017), no. 1, 196--211 [HAL] [DOI]
6. Integrability conditions on coboundary and transfer function for limit theorems - ALEA, Lat. Am. J. Probab. Math. Stat. 13(1) (2016), 399–415 [HAL] [DOI]
5. Holderian weak invariance principle under a Hannan type condition - Stochastic Processes and their Applications 126 (2016), 290-311 [HAL] [DOI]
4. Orthomartingale-coboundary decomposition for stationary random fields Mohamed El Machkouri Stochastics and Dynamics 16 (2016), no. 5, 1650017, 28 pp. [HAL] [DOI]
3. An improvement of the mixing rates in a counter-example to the weak invariance principle - Comptes Rendus de l'Académie des Sciences 353 (2015), 953-958 [HAL] [DOI]
2. A strictly stationary \(\beta\)-mixing process satisfying the central limit theorem but not the weak invariance principle Dalibor Volný Stochastic Processes and their Applications 124 (2014), 3769-3781 [Arxiv] [DOI]
1. A counter example to the central limit theorem in Hilbert spaces under a strong mixing condition Dalibor Volný Electronic Communications in Probability 19 (2014) [Arxiv], [HAL] [DOI]