Deviation inequalities for sums of weakly dependent time series

Olivier Wintenberger (1)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

In this paper we give new deviation inequalities of Bernstein's type for the partial sums of weakly dependent time series. The loss from the independent case is studied carefully. We give non mixing examples such that dynamical systems and Bernoulli shifts for whom our deviation inequalities hold. The proofs are based on the blocks technique and different coupling arguments.

Mots clés: Exponential inequality; weak dependence; coupling scheme; dynamical systems; Bernoulli schifts

Domaines: Probabilités [math.PR]

Olivier Wintenberger. Deviation inequalities for sums of weakly dependent time series. Electronic Communications in Probability, 2010, 15, pp.489-503. ⟨hal-00430608⟩