D. Giraudo

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math.PR2020

Bound on the maximal function associated to the bounded law of the iterated logarithms via orthomartingale approximation

Davide Giraudo

We give sufficient conditions for the bounded law of the iterated logarithms for strictly stationary random fields when the summation is done on rectangle. The study is done by the…

math.PR2019

An exponential inequality for $U$ -statistics of i.i.d. data

Davide Giraudo

We establish an exponential inequality for degenerated $U$ -statistics of order $r$ of i.i.d. data. This inequality gives a control of the tail of the maxima absolute values of the…

math.PR2019

Large deviation inequalities for martingales in Banach spaces

Xiequan Fan, Davide Giraudo

Let $(X_{i}, F_{i})_{i \geq 1}$ be a martingale difference sequence in a smooth Banach space. Let $S_{n} = \sum_{i = 1}^{n} X_{i}, n \geq 1,$ be the partial sums of $(X_i, \mathcal{F}_i)_{…

math.PR2019

Limit theorems for U-statistics of Bernoulli data

Davide Giraudo

In this paper, we consider U-statistics whose data is a strictly stationary sequence which can be expressed as a functional of an i.i.d. one. We establish a strong law of large num…

Bound on the maximal function associated to the bounded law of the iterated logarithms via orthomartingale approximation

An exponential inequality for U-statistics of i.i.d. data

Large deviation inequalities for martingales in Banach spaces

Limit theorems for U-statistics of Bernoulli data

An exponential inequality for $U$ -statistics of i.i.d. data