Related papers: Nonconventional moderate deviations theorems and e…

We obtain Berry-Esseen type estimates for "nonconventional" expressions of the form $\xi_N=\frac 1{\sqrt N}\sum_{n=1}^N(F(X(q_1(n)),...,X(q_\ell(n)))-\bar F)$

We obtain almost optimal convergence rate in the central limit theorem for "nonconevntional" sums of the form $S_N=N^{-\frac12}\sum_{n=1}^N (F(\xi_n,\xi_{2n},...,\xi_{\ell n})-\bar F)$.

We extend local limit theorem type results to nonconventional sums of the form $S_N=\sum_{n=1}^NF(\xi_n,\xi_{2n},...,\xi_{\ell n})$.

Initially motivated by the study of the non-asymptotic properties of non-parametric tests based on permutation methods, concentration inequalities for uniformly permuted sums have been largely studied in the literature. Recently, Delyon et…

For a real-valued measurable function $f$ and a nonnegative, nondecreasing function $\phi$, we first obtain a Chebyshev type inequality which provides an upper bound for $\displaystyle \phi(\lambda_{1}) \mu(\{x \in \Omega : f(x) \geq…

We obtain large deviations theorems for nonconventional sums with underlying process being a Markov process satisfying the Doeblin condition or a dynamical system such as subshift of finite type or hyperbolic or expanding transformation.

We consider the stochastic integrals of multivariate point processes and study their concentration phenomena. In particular, we obtain a Bernstein type of concentration inequality through Dol\'eans-Dade exponential formula and a uniform…

This paper deals with strong invariance principles (known also as strong approximation theorems) for sums of the form $\sum_{n=1}^{[Nt]}F\big(X(n),X(2n),...,X(kn), X(q_{k+1}(n)),X(q_{k+2}(n)),..., X(q_\ell(n))\big)$

In this paper we obtain a Bernstein type inequality for a class of weakly dependent and bounded random variables. The proofs lead to a moderate deviations principle for sums of bounded random variables with exponential decay of the strong…

We obtain rge Erd\" os-R\' enyi type law of large numbers for "nonconventional" sums of the form $S_n=\sum^n_{m=1}F(X_m,X_{2m},...,X_{\ell m})$ where $X_1,X_2,...$ is a sequence of i.i.d. random variables and $F$ is a bounded Borel…

We obtain a functional central limit theorem (CLT) for sums of the form $\xi_N(t)=\frac1{\sqrt N}\sum_{n=1}^{[Nt]}\big(F(X(q_1(n)),...,X(q_\ell(n)))-\bar F\big)$ where $q_1,...,q_\ell$ are polynomials.

We give a distribution-dependent concentration inequality for functions of independent variables. The result extends Bernstein's inequality from sums to more general functions, whose variation in any argument does not depend too much on the…

We obtain functional central limit theorems for both discrete time expressions of the form $1/\sqrt{N}\sum_{n=1}^{[Nt]}(F(X(q_1(n)),\ldots, X(q_{\ell}(n)))-\bar{F})$ and similar expressions in the continuous time where the sum is replaced…

We derive concentration inequalities for empirical means $\frac{1}{t} \int_0^t f(X_s) ds$ where $X_s$ is an irreducible Markov jump process on a finite state space and $f$ some observable. Using a Feynman-Kac semigroup we first derive a…

For a wide class of monotonic functions $f$, we develop a Chernoff-style concentration inequality for quadratic forms $Q_f \sim \sum\limits_{i=1}^n f(\eta_i) (Z_i + \delta_i)^2$, where $Z_i \sim N(0,1)$. The inequality is expressed in terms…

The term moderate deviations is often used in the literature to mean a class of large deviation principles that, in some sense, fills the gap between a convergence in probability of some random variables to a constant and a weak convergence…

Concentration inequalities quantify the deviation of a random variable from a fixed value. In spite of numerous applications, such as opinion surveys or ecological counting procedures, few concentration results are known for the setting of…

We study concentration inequalities for structured weighted sums of random data, including (i) tensor inner products and (ii) sequential matrix sums. We are interested in tail bounds and concentration inequalities for those structured…

This work obtains sharp closed-form exponential concentration inequalities of Bernstein type for the ubiquitous beta distribution, improving upon sub-gaussian and sub-gamma bounds previously studied in this context. The proof leverages a…

For noncorrelated random variables, we study a concentration property of the family of distributions of normalized sums formed by sequences of times of a given large length.