Dual Lukacs regressions for non-commutative variables

Dual Lukacs type characterizations of random variables in free probability are studied here. First, we develop a freeness property satisfied by Lukacs type transformations of free-Poisson and free-binomial non-commutative variables which are free. Second, we give a characterization of non-commutative free-Poisson and free-binomial variables by properties of first two conditional moments, which mimic Lukacs type assumptions known from classical probability. More precisely, our result is a non-commutative version of the following result known in classical probability: if U, V   are independent real random variables, such that E(V(1−U)|UV)$\mathbb{E}(V(1-U)|UV)$ and E(V²(1−U)²|UV)$\mathbb{E}(V^2{(1-U)}^2|UV)$ are non-random then V has a gamma distribution and U has a beta distribution.     

An existence theorem for the Scheinkman-Weiss economic model

The Scheinkman-Weiss model and later works by Conze-Lasry-Scheinkman provide insights on cycles and correlations of economies with incomplete markets, namely with borrowing constraints. This work gives a mathematical solution in the case of high relative risk aversion, which has not yet been solved. The existence of an equilibrium results from the solution of a system of nonlinear functional differential equations. High risk aversion leads to new mathematical difficulties, not present in previous papers on this subject.This work is an extension of previous works done under the direction of Professor Jean-Michel Lasry, University of Paris 9, Dauphine. The author is sincerely grateful to Professor Lasry who suggested the idea of this article and whose remarks were always of help.     

Gamma分布与其它分布的若干定理

利用条件概率的性质,得到Gamma分布与Poisson分布、广义负二项分布、广义Pareto分布的若干定理及推论.     

Multivariate irregular sampling theorem

In this paper,we prove a Marcinkiewicz-Zygmund type inequality for multivariate entire functions of exponential type with non-equidistant spaced sampling points. And from this result,we establish a multivariate irregular Whittaker-Kotelnikov-Shannon type sampling theorem.     

Floquet theorem for linear implicit nonautonomous difference systems

The aim of this paper is to develop the Floquet theory for linear implicit difference systems (LIDS). It is proved that any index-1 LIDS can be transformed into its Kronecker normal form. Then the Floquet theorem on the representation of the fundamental matrix of index-1 periodic LIDS has been established. As an immediate consequence, the Lyapunov reduction theorem is proved. Some applications of the obtained results are discussed.     

Bivariate distributions via a Pareto conditional distribution and a regression function

Uniqueness of specification of a bivariate distribution by a Pareto conditional and a consistent regression function is investigated. New characterizations of the Mardia bivariate Pareto distribution and the bivariate Pareto conditionals distribution are obtained.     

On Osgood theorem in Banach spaces

Let X be a real Banach space, ω : [0, +∞) → ? be an increasing continuous function such that ω(0) = 0 and ω(t + s) ≤ ω(t) + ω(s) for all t, s ∈ [0, +∞). According to the infinite dimensional analog of the Osgood theorem if ∫¹₀ (ω(t))^?1 dt = ∞, then for any (t₀, x₀) ∈ ?×X and any continuous map f : ?×X → X such that ∥f(t, x) – f(t, y)∥ ≤ ω(∥x – y∥) for all t ∈ ?, x, y ∈ X, the Cauchy problem (t) = f(t, x(t)), x(t₀) = x₀ has a unique solution in a neighborhood of t₀. We prove that if X has a complemented subspace with an unconditional Schauder basis and ∫¹₀ (ω(t))^?1 dt < ∞ then there exists a continuous map f : ? × X → X such that ∥f(t, x) – f(t, y)∥ ≤ ω(∥x – y∥) for all (t, x, y) ∈ ? × X × X and the Cauchy problem (t) = f(t, x(t)), x(t₀) = x₀ has no solutions in any interval of the real line.     

A comparison theorem and uniqueness theorem of backward doubly stochastic differential equations

In this paper, we deal with one dimensional backward doubly stochastic differential equations (BDSDEs). We obtain a comparison theorem and a uniqueness theorem for BDSDEs with continuous coefficients.     

A Schauder-type fixed point theorem

In this brief note we study Schauder's second fixed point theorem in the space $(\mathit{BC},6\cdot 6)$ of bounded continuous functions $\varphi :[0,\infty )\to {\Re }^n$ with a view to reducing the requirement that there is a compact map to the requirement that the map is locally equicontinuous. Several examples are given, both motivating and applying the theory.     

A new conservation theorem

A general theorem on conservation laws for arbitrary differential equations is proved. The theorem is valid also for any system of differential equations where the number of equations is equal to the number of dependent variables. The new theorem does not require existence of a Lagrangian and is based on a concept of an adjoint equation for non-linear equations suggested recently by the author. It is proved that the adjoint equation inherits all symmetries of the original equation. Accordingly, one can associate a conservation law with any group of Lie, Lie-Bäcklund or non-local symmetries and find conservation laws for differential equations without classical Lagrangians.     

条件Erlang分布的双参数加法定理

X(γ)和Y(k)服从参数(γ,λ)和(k,μ)的Erlang分布且相互独立.本文证明了在X(γ)相似文献   

Generalization of Erdős-Kac theorem

Let ω(n) is the number of distinct prime factors of the natural number n,we consider two cases where \ell is even and odd natural numbers, and then we prove a more general form of the classical Erdős-Kac theorem.     

Peano type theorem for abstract parabolic equations

We consider parabolic problems with non-Lipschitz nonlinearity in the different scales of Banach spaces and prove local-in-time existence theorem.     

A Liouville-type theorem for the stationary MHD equations

We establish a new Liouville-type theorem for solutions of the stationary MHD equations imposing asymmetric oscillation growth conditions on the tensor-valued functions for the velocity and the magnetic field.     

Second main theorem and uniqueness theorem with moving targets on parabolic manifolds

In this paper, with the motivation from Diophantine approximation, a truncated second main theorem is established for meromorphic maps from M   into P(V)$\mathbb{P}(V)$ with moving targets _gj:M→P(V^?)$g_j:M\to \mathbb{P}(V^{?})$, 1≤j≤q$1\le j\le q$, where M is a parabolic manifold and V is a Hermitian vector space. As an application of this second main theorem, a uniqueness theorem without counting multiplicities is given.     

Massera-Type theorem and asymptotically periodic Logistic equations

Some important properties of asymptotically periodic functions were studied in this paper. Sufficient conditions of existence of globally stable asymptotically periodic solution were obtained. Then, Massera-Type theorems were discussed for one-dimensional, two-dimensional, higher-dimensional asymptotically periodic systems. Finally, global stability of periodic Logistic equations and asymptotically periodic Logistic equations were considered, respectively.     

A mean-value theorem and its applications

For a function f defined in an interval I, satisfying the conditions ensuring the existence and uniqueness of the Lagrange mean L[f], we prove that there exists a unique two variable mean M[f] such that