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Deviation inequalities for dependent sequences with applications to strong approximations

Author

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  • Dedecker, Jérôme
  • Merlevède, Florence
  • Rio, Emmanuel

Abstract

In this paper, we give precise rates of convergence in the strong invariance principle for stationary sequences of bounded real-valued random variables satisfying weak dependence conditions. One of the main ingredients is a new Fuk-Nagaev type inequality for a class of weakly dependent sequences. We describe also several classes of processes to which our results apply.

Suggested Citation

  • Dedecker, Jérôme & Merlevède, Florence & Rio, Emmanuel, 2024. "Deviation inequalities for dependent sequences with applications to strong approximations," Stochastic Processes and their Applications, Elsevier, vol. 174(C).
  • Handle: RePEc:eee:spapps:v:174:y:2024:i:c:s0304414924000838
    DOI: 10.1016/j.spa.2024.104377
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