Concentration of the spectral measure for large random matrices with stable entries.
Conditional principles for random weighted measures
In this paper, we prove a conditional principle of Gibbs type for random weighted measures of the form , being a sequence of i.i.d. real random variables. Our work extends the preceding results of Gamboa and Gassiat (1997), in allowing to consider thin constraints. Transportation-like ideas are used in the proof.
Conditional principles for random weighted measures
In this paper, we prove a conditional principle of Gibbs type for random weighted measures of the form , ((Zi)i being a sequence of i.i.d. real random variables. Our work extends the preceding results of Gamboa and Gassiat (1997), in allowing to consider thin constraints. Transportation-like ideas are used in the proof.
Convergence of stopped sums of weakly dependent random variables.
Convex concentration inequalities and forward-backward stochastic calculus.
Convexity inequalities for estimating generalized conditional entropies from below
Generalized entropic functionals are in an active area of research. Hence lower and upper bounds on these functionals are of interest. Lower bounds for estimating Rényi conditional -entropy and two kinds of non-extensive conditional -entropy are obtained. These bounds are expressed in terms of error probability of the standard decision and extend the inequalities known for the regular conditional entropy. The presented inequalities are mainly based on the convexity of some functions. In a certain...
Convolution property and exponential bounds for symmetric monotone densities
Our first theorem states that the convolution of two symmetric densities which are k-monotone on (0,∞) is again (symmetric) k-monotone provided 0 < k ≤ 1. We then apply this result, together with an extremality approach, to derive sharp moment and exponential bounds for distributions having such shape constrained densities.
Correction to "Prophet inequalities for averages of independent non-negative random variables".
Correlation measures.
Cyclic random inequalities
Davis-type inequalities for a number of diffusion processes.
Detecting abrupt changes in random fields
This paper is devoted to the study of some asymptotic properties of a -estimator in a framework of detection of abrupt changes in random field’s distribution. This class of problems includes e.g. recovery of sets. It involves various techniques, including -estimation method, concentration inequalities, maximal inequalities for dependent random variables and -mixing. Penalization of the criterion function when the size of the true model is unknown is performed. All the results apply under mild,...
Detecting abrupt changes in random fields
This paper is devoted to the study of some asymptotic properties of a M-estimator in a framework of detection of abrupt changes in random field's distribution. This class of problems includes e.g. recovery of sets. It involves various techniques, including M-estimation method, concentration inequalities, maximal inequalities for dependent random variables and ϕ-mixing. Penalization of the criterion function when the size of the true model is unknown is performed. All the results apply under...
Determinantal probability measures
Determinantal point processes have arisen in diverse settings in recent years and have been investigated intensively. We study basic combinatorial and probabilistic aspects in the discrete case. Our main results concern relationships with matroids, stochastic domination, negative association, completeness for infinite matroids, tail triviality, and a method for extension of results from orthogonal projections to positive contractions. We also present several new avenues for further investigation,...
Difference of general integral means.
Directionally convex ordering in multidimensional jump diffusions models.
Dispersive functions and stochastic orders
Generalizations of the hazard functions are proposed and general hazard rate orders are introduced. Some stochastic orders are defined as general ones. A unified derivation of relations between the dispersive order and some other orders of distributions is presented
Distance de Fortet-Mourier et fonctions log-concaves
Doob's type inequality and strong law of large numbers for demimartingales.
Dynamic dependence ordering for Archimedean copulas and distorted copulas
This paper proposes a general framework to compare the strength of the dependence in survival models, as time changes, i. e. given remaining lifetimes , to compare the dependence of given , and given , where . More precisely, analytical results will be obtained in the case the survival copula of is either Archimedean or a distorted copula. The case of a frailty based model will also be discussed in details.