• Corpus ID: 210839190

Optimal Gaussian concentration bounds for stochastic chains of unbounded memory

@article{Chazottes2020OptimalGC,
  title={Optimal Gaussian concentration bounds for stochastic chains of unbounded memory},
  author={Jean-Ren{\'e} Chazottes and Sandro Gallo and Daniel Y. Takahashi},
  journal={arXiv: Probability},
  year={2020}
}
We obtain explicit and optimal Gaussian concentration bounds (GCBs) for stochastic chains of unbounded memory (SCUMs) on countable alphabets. These stochastic processes are also known as "chains with complete connections" or "g-measures". We prove that a GCB holds when the sum of oscillations of the kernel is less than one, or when the variation of the kernel is summable, i.e., belongs to l^1(N). The proof is based on maximal coupling. Our conditions are optimal in the sense that we exhibit… 

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