Doubly stochastic operators on a finite-dimensional simplex

Generalizing the concept of a quadratic doubly stochastic operator, we introduce the concept of an arbitrary doubly stochastic operator. We give a necessary condition for double stochasticity. Moreover, we prove an ergodic theorem for doubly stochastic operators. Original Russian Text Copyright ? 2009 Shahidi F. A. __________ Tashkent. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 50, No. 2, pp. 463–468, March–April, 2009.     

Conditional cubic stochastic operator

We introduce the concept of conditional cubic stochastic operator in this study. We show that any conditional cubic stochastic operator has a unique fixed point and such an operator has the property of being regular.     

具有位数3和4的双随机循环矩阵中的素元

本文研究了双随机循环矩阵中素元的分类问题．由于任一n阶双随机循环矩阵都可以唯一地表示为移位的n-1次一元多项式,从而可把双随机循环矩阵中素元的分类问题简化为解双随机循环矩阵上的一个方程．应用此原理,本文完全解决了判别具有位数3的n阶双随机循环矩阵是否为素元的问题,并给出了n阶双随机循环矩阵中一类具有位数4的素元．     

A First-Order Stochastic Primal-Dual Algorithm with Correction Step

In this article, we investigate the convergence properties of a stochastic primal-dual splitting algorithm for solving structured monotone inclusions involving the sum of a cocoercive operator and a composite monotone operator. The proposed method is the stochastic extension to monotone inclusions of a proximal method studied in the literature for saddle point problems. It consists in a forward step determined by the stochastic evaluation of the cocoercive operator, a backward step in the dual variables involving the resolvent of the monotone operator, and an additional forward step using the stochastic evaluation of the cocoercive operator introduced in the first step. We prove weak almost sure convergence of the iterates by showing that the primal-dual sequence generated by the method is stochastic quasi-Fejér-monotone with respect to the set of zeros of the considered primal and dual inclusions. Additional results on ergodic convergence in expectation are considered for the special case of saddle point models.     

Eigenvalue Problem of Doubly Stochastic Hamiltonian Systems with Boundary Conditions

In this paper, we investigate the eigenvalue problem of forward-backward doubly stochastic dii~erential equations with boundary value conditions. We show that this problem can be represented as an eigenvalue problem of a bounded continuous compact operator. Hence using the famous Hilbert-Schmidt spectrum theory, we can characterize the eigenvalues exactly.     

Stochastic bilinear spectral systems †

A class of bilinear stochastic partial differential equations is investigated using a semigroup approach. Existence of a mild solution is obtained by proving a maximal inequality for stochastic convolution integrals with a stochastic evolution operator U(t,s) as integrand; moreover, we show the existence of a regular version in t. Under an additional assumption we show the existence of a continuous version of U (.,.) in the space of bounded operators on the state space. Finally, we analyse a p.d.e. model of a simply supported beam to illustrate the applicability of our results to modelling uncertainty in large flexible space structures     

Vertex degrees and doubly stochastic graph matrices

In this article, the relationship between vertex degrees and entries of the doubly stochastic graph matrix has been investigated. In particular, we present an upper bound for the main diagonal entries of a doubly stochastic graph matrix and investigate the relations between a kind of distance for graph vertices and the vertex degrees. These results are used to answer in negative Merris' question on doubly stochastic graph matrices. These results may also be used to establish relations between graph structure and entries of doubly stochastic graph matrices. © 2010 Wiley Periodicals, Inc. J Graph Theory 66:104‐114, 2011     

一类随机非自伴波方程的半离散有限元近似

本文研究了由白噪音驱动的随机非自伴波方程的有限元近似,由于线性算子A非自伴,不能应用A的特征值和特征向量,从而得到的结果更具有一般性.空间离散上采用标准的有限元法,并借助强连续算子函数的性质,得到了该方程的强收敛误差估计.本文方法也适用于多维情况的分析.最后用数值算例验证了理论分析的正确性.     

广义双随机矩阵反问题及其应用

研究广义双随机矩阵反问题.给出广义双随机矩阵的最小二乘解,得到了解的具体表达形式.并讨论了用广义双随机矩阵构造给定矩阵的最佳逼近问题,给出该问题有解的充分必要条件和解的表达形式.包括算法及数值例子.     

基于随机模拟视角的混合数据形式密度算子

基于“蒙特卡罗仿真”的思想,采用随机模拟的方法从混合数据形式的角度对密度算子进行拓展研究。首先,给出了一种将混合数据转化为区间数的方法,并通过平移和放大或缩小处理,将所有区间数放到同一区间范围内;然后,运用随机数发生器给出区间上某分布的随机数信息,并依据随机数的分布情况对其进行聚类,给出了密度权重的确定方法;在此基础上,将随机模拟的方法应用于密度算子信息集结模型中,得到带有概率信息的评价结论。最后,通过一个算例验证了方法的有效性。     

A BSDE approach to Nash equilibrium payoffs for stochastic differential games with nonlinear cost functionals

In this paper, we study Nash equilibrium payoffs for two-player nonzero-sum stochastic differential games via the theory of backward stochastic differential equations. We obtain an existence theorem and a characterization theorem of Nash equilibrium payoffs for two-player nonzero-sum stochastic differential games with nonlinear cost functionals defined with the help of doubly controlled backward stochastic differential equations. Our results extend former ones by Buckdahn et al. (2004) [3] and are based on a backward stochastic differential equation approach.     

A Stochastic Filtering Approach To Survival Analysis

We connect some basic issues in survival analysis in biostatistics with estimation and convergence theories in stochastic filtering. Viewing censored data problems through a filtering perspective, we can derive estimators expressed using stochastic integral/differential equations. We then study statistical asymptotic using convergence theory of stochastic equations. We illustrate the effectiveness of such a program by revisiting the right censored and the doubly censored data problems.     

On a Lie-theoretic approach to generalized doubly stochastic matrices and applications

In this article, we study generalized doubly stochastic matrices using the theory of Lie groups and Lie algebras. Applications to the inverse eigenvalue problem for symmetric doubly stochastic matrices are presented.     

On a Lie-theoretic approach to generalized doubly stochastic matrices and applications

In this article, we study generalized doubly stochastic matrices using the theory of Lie groups and Lie algebras. Applications to the inverse eigenvalue problem for symmetric doubly stochastic matrices are presented.     

带跳的分数倒向重随机微分方程及相应的随机积分偏微分方程

本文首次把Poisson随机测度引入分数倒向重随机微分方程,基于可料的Girsanov变换证明由Brown运动、Poisson随机测度和Hurst参数在(1/2,1)范围内的分数Brown运动共同驱动的半线性倒向重随机微分方程解的存在唯一性.在此基础上,本文定义一类半线性随机积分偏微分方程的随机黏性解,并证明该黏性解由带跳分数倒向重随机微分方程的解唯一地给出,对经典的黏性解理论作出有益的补充.     

Optimal Solutions of Fractional Nonlinear Impulsive Neutral Stochastic Functional Integro-Differential Equations

Abstract

In this article, we consider a new class of fractional impulsive neutral stochastic functional integro-differential equations with infinite delay in Hilbert spaces. First, by using stochastic analysis, fractional calculus, analytic α-resolvent operator and suitable fixed point theorems, we prove the existence of mild solutions and optimal mild solutions for these equations. Second, the existence of optimal pairs of system governed by fractional impulsive partial stochastic integro-differential equations is also presented. The results are obtained under weaker conditions in the sense of the fractional power arguments. Finally, an example is given for demonstration.     

Multi‐valued backward stochastic differential equations driven by G‐Brownian motion and its applications

In this paper, we prove the existence and uniqueness of a solution for a class of backward stochastic differential equations driven by G‐Brownian motion with subdifferential operator by means of the Moreau–Yosida approximation method. Moreover, we give a probabilistic interpretation for the viscosity solutions of a kind of nonlinear variational inequalities. Copyright © 2017 John Wiley & Sons, Ltd.     

Large deviation for mean-field stochastic differential equations with subdifferential operator

In this article, we prove the existence and uniqueness of a solution for a class of mean-field stochastic differential equations with subdifferential operator (i.e., mean-field MSDEs) by means of the Moreau–Yosida type penalization method. Moreover, we prove a large deviation principle of its path solution via the weak convergence method.     

On constrained Volterra cubic stochastic operators

We consider constrained Volterra cubic stochastic operators and construct several Lyapunov functions for the constrained Volterra cubic stochastic operators. We prove that such kind operators do not have periodic trajectories. Finally, we show that the set of all constrained Volterra cubic stochastic operators is a convex compact set and find the extreme points of this set.     

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.