For a stochastic process with state space some Polish space, this paper gives sufficient conditions on the initial and conditional distributions for the joint law to satisfy Gaussian concentration inequalities and transportation inequalities. In the case of the Euclidean space ${ℝ}^m$, there are sufficient conditions for the joint law to satisfy a logarithmic Sobolev inequality. In several cases, the constants obtained are of optimal order of growth with respect to the number of random variables, or are...

In this paper, we prove a conditional principle of Gibbs type for random weighted measures of the form $L_n=\frac{1}{n}{\sum }_{i=1}^n{Z}_i{\delta }_{x_i^n}$, ${\left(Z_i\right)}_i$ 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.

In this paper, we prove a conditional principle of Gibbs type for random weighted measures of the form $L_n=\frac{1}{n}{\sum }_{i=1}^n{Z}_i{\delta }_{x_i^n}$, ((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.

Conditions for bimodality of mixtures of two unimodal distributions are investigated in some special cases. Based on general characterizations, explicit criteria for the parameters are derived for mixtures of two Cauchy, logistic, Student, gamma, log-normal, Gumbel and other distributions.

Let (X1,Y1),...,(Xm,Ym) be m independent identically distributed bivariate vectors and L1 = β1X1 + ... + βmXm, L2 = β1X1 + ... + βmXm are two linear forms with positive coefficients. We study two problems: under what conditions does the equidistribution of L1 and L2 imply the same property for X1 and Y1, and under what conditions does the independence of L1 and L2 entail independence of X1 and Y1? Some analytical sufficient conditions are obtained and it is shown that in general they can not be...

Let $(X_1,Y_1),...,(X_m,Y_m)$ be $m$ independent identically distributed bivariate vectors and $L_1={\beta }_1{X}_1+...+{\beta }_m{X}_m$, $L_2={\beta }_1{Y}_1+...+{\beta }_m{Y}_m$ are two linear forms with positive coefficients. We study two problems: under what conditions does the equidistribution of $L_1$ and $L_2$ imply the same property for $X_1$ and $Y_1$, and under what conditions does the independence of $L_1$ and $L_2$ entail independence of $X_1$ and $Y_1$? Some analytical sufficient conditions are obtained and it is shown that in general they can not be weakened.

In this paper, we introduce two transformations on a given copula to construct new and recover already-existent families. The method is based on the choice of pairs of order statistics of the marginal distributions. Properties of such transformations and their effects on the dependence and symmetry structure of a copula are studied.

The number of $n$-gaussoids is shown to be a double exponential function in $n$. The necessary bounds are achieved by studying construction methods for gaussoids that rely on prescribing $3$-minors and encoding the resulting combinatorial constraints in a suitable transitive graph. Various special classes of gaussoids arise from restricting the allowed $3$-minors.

In this paper we give an alternative proof of the construction of $n$-dimensional ordinal sums given in Mesiar and Sempi [17], we also provide a new methodology to construct $n$-copulas extending the patchwork methodology of Durante, Saminger-Platz and Sarkoci in [6] and [7]. Finally, we use the gluing method of Siburg and Stoimenov [20] and its generalization in Mesiar et al. [15] to give an alternative method of patchwork construction of $n$-copulas, which can be also used in composition with our patchwork...

The construction of multivariate distributions is an active field of research in theoretical and applied statistics. In this paper some recent developments in this field are reviewed. Specifically, we study and review the following set of methods: (a) Construction of multivariate distributions based on order statistics, (b) Methods based on mixtures, (c) Conditionally specified distributions, (d) Multivariate skew distributions, (e) Distributions based on the method of the variables in common and...

We continue the investigation started in a previous paper, on weak convergence to infinitely divisible distributions with finite variance. In the present paper, we study this problem for some weakly dependent random variables, including in particular associated sequences. We obtain minimal conditions expressed in terms of individual random variables. As in the i.i.d. case, we describe the convergence to the gaussian and the purely non-gaussian parts of the infinitely divisible limit. We also discuss...