In this paper, we study the risk bounds for samples independently drawn from an infinitely divisible (ID) distribution. In particular, based on a martingale method, we develop two deviation inequalities for a sequence of random variables of an ID distribution with zero Gaussian component. By applying the deviation inequalities, we obtain the risk bounds based on the covering number for the ID d...

We prove that many of beta, beta prime, gamma, inverse gamma, Student tand ultraspherical distributions are freely infinitely divisible, but some of them are not. The latter negative result follows from a local property of probability density functions. Moreover, we show that the Gaussian, many of ultraspherical and Student t-distributions have free divisibility indicator 1.

We consider the \(p\)-Laplacian system $$ \displaylines{ -\Delta_p u = \lambda f(v) \quad \text{in } \Omega; \cr v g(u) v=0 \text{on }\partial \Omega, }$$ where \(\lambda >0\) is a parameter, \(\Delta_p u:= \operatorname{div}(|\nabla u|^{p-2}\nabla u)\) operator for \(p > 1\) and \(\Omega\) unit ball in \(\mathbb{R}^N\) (\(N \geq 2)\). The nonlinearities \(f, g: [0,\infty) \to \mathbb{R}\...

in this paper, we introduce and study a mixed variational inclusion problem involving infinite family of fuzzy mappings. an iterative algorithm is constructed for solving a mixed variational inclusion problem involving infinite family of fuzzy mappings and the convergence of iterative sequences generated by the proposed algorithm is proved. some illustrative examples are also given.

a normed space $mathfrak{x}$ is said to have the fixed point property, if for each nonexpansive mapping $t : e longrightarrow e $ on a nonempty bounded closed convex subset $ e $ of $ mathfrak{x} $ has a fixed point. in this paper, we first show that if $ x $ is a locally compact hausdorff space then the following are equivalent: (i) $x$ is infinite set, (ii) $c_0(x)$ is infinite dimensional, (...

Let $R$ be an infinite ring. Here we prove that if $0_R$ belongs to ${x_1x_2cdots x_n ;|; x_1,x_2,dots,x_nin X}$ for every infinite subset $X$ of $R$, then $R$ satisfies the polynomial identity $x^n=0$. Also we prove that if $0_R$ belongs to ${x_1x_2cdots x_n-x_{n+1} ;|; x_1,x_2,dots,x_n,x_{n+1}in X}$ for every infinite subset $X$ of $R$, then $x^n=x$ for all $xin R$.

This study is concerned with the formulation of three dimensional mapped infinite elements with 1/r and 1/ decay types. These infinite elements are coupled with conventional finite elements and their application to some problems of soil structure interaction are discussed. The effeciency of the coupled finite-infinite elements formulation with respect to computational effort, data preparation a...

The paper is concerned with algebras whose elements can be used to represent runs of a system from a state to a state. These algebras, called multiplicative transition systems, are categories with respect to a partial binary operation called composition. They can be characterized by axioms such that their elements and operations can be represented by partially ordered multisets of a certain typ...

We prove that the q-Gaussian distribution is freely infinitely divisible for all q ∈ [0, 1].

We give an infinite family of functions involving the gamma function whose logarithmic derivatives are completely monotonic. Each such function gives rise to an infinitely divisible probability distribution. Other similar results are also obtained for specific combinations of the gamma and q-gamma functions.