Moments of integral-type downward functionals for single death processes

We get an explicit and recursive representation for high order moments of integral-type downward functionals for single death processes. Meanwhile, main results are applied to more general integral-type downward functionals.     

On duality for mathematical programs with vanishing constraints

We make a review of several variants of ergodicity for continuous-time Markov chains on a countable state space. These include strong ergodicity, ergodicity in weighted-norm spaces, exponential and subexponential ergodicity. We also study uniform exponential ergodicity for continuous-time controlled Markov chains, as a tool to deal with average reward and related optimality criteria. A discussion on the corresponding ergodicity properties is made, and an application to a controlled population system is shown.     

Ergodicity of a polling network with an infinite number of stations

A Markov polling system with infinitely many stations is studied. The topic is the ergodicity of the infinite-dimensional process of queue lengths. For the infinite-dimensional process, the usual type of ergodicity cannot prevail in general and we introduce a modified concept of ergodicity, namely, weak ergodicity. It means the convergence of finite-dimensional distributions of the process. We give necessary and sufficient conditions for weak ergodicity. Also, the “usual” ergodicity of the system is studied, as well as convergence of functionals which are continuous in some norm. This revised version was published online in June 2006 with corrections to the Cover Date.     

Asymptotic normality of spherical means of nonlinear functionals of Gaussian random fields

The central limit theorem is proved for the integral-type functionals of nonlinear transformations of two-and three-dimensional uniform isotropic Gaussian random fields. A theorem on convergence of finite-dimensional distributions of these functionals to the corresponding distributions of the Wiener process is also established.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 4, pp. 472–480, April, 1993.     

On the subexponentiality of the ridgelet transform

We show that we can consider the ridgelet transform for Wiener functionals as a subexponential random variable. We give an application of this result to random walks.     

股票收益率的次指数分布拟合

股票收益率等金融时间序列具有重尾特征,因而不适于用正态分布来描述,次指数分布族S是一类重尾分布族,能够很好的处理具有偏态、重尾特征的金融时间序列,本文对上证指数的收益率进行了次指数分布拟合,并给出了在险价值(VaR)的估计。     

Functional estimation for Lévy measures of semimartingales with Poissonian jumps

We consider semimartingales with jumps that have finite Lévy measures. The purpose of this article is to estimate integral-type functionals of the Lévy measures from discrete observations. We propose two types of estimators: kernel-type and empirical-type estimators, both of which are obtained by direct discretization from asymptotically efficient estimators of the target based on continuous observations. We show the asymptotic efficiency in the asymptotic minimax sense of our estimators as the sample size tends to infinity and the sampling interval tends to zero.     

Ergodic Control of a Singularly Perturbed Markov Process in Discrete Time with General State and Compact Action Spaces

Ergodic control of singularly perturbed Markov chains with general state and compact action spaces is considered. A new method is given for characterization of the limit of invariant measures, for perturbed chains, when the perturbation parameter goes to zero. It is also demonstrated that the limit control principle is satisfied under natural ergodicity assumptions about controlled Markov chains. These assumptions allow for the presence of transient states, a situation that has not been considered in the literature before in the context of control of singularly perturbed Markov processes with long-run-average cost functionals. Accepted 3 December 1996     

Practical scaled consensus for nonlinear multiagent systems with input time delay via a new distributed integral-type event-triggered scheme

This paper studies scaled-based practical consensus issue for multiagent systems with input time delay by a fully continuous communication-free integral-type event-triggered scheme. By choosing the proper scales, scaled consensus can be induced to synchronization, bipartite consensus or cluster consensus. By defining a continuous communication-free measurement error for the integral-type event-triggered mechanism, the new integral-type event-triggered condition is proposed which can not only reduce the energy consumption but also prolong the interevent time. Then, with time domain analysis method, the distributed integral-type event-triggered control problem for nonlinear general multiagent systems involving input time delay is investigated and then the second-order counterpart, with a calculated upper-bound for time-delay. Moreover, it is concluded that with such event-triggered protocols, practical scaled consensus can be achieved without the exhibition of Zeno behavior. At last, simulations are shown to support the results.     

Two Non-closure Properties on the Class of Subexponential Densities

Relations between subexponential densities and locally subexponential distributions are discussed. It is shown that the class of subexponential densities is neither closed under convolution roots nor closed under asymptotic equivalence. A remark is given on the closure under convolution roots for the class of convolution equivalent distributions.     

Random matrices and subexponential operator spaces

We introduce and study a generalization of the notion of exact operator space that we call subexponential. Using Random Matrices we show that the factorization results of Grothendieck type that are known in the exact case all extend to the subexponential case, but we exhibit (a continuum of distinct) examples of non-exact subexponential operator spaces, as well as a C*-algebra that is subexponential with constant 1 but not exact. We also show that OH, R + C and max(?₂) (or any other maximal operator space) are not subexponential.     

On the stable difference scheme for source identification nonlocal elliptic problem

Approximation of source identification problem for elliptic equation with integral-type nonlocal condition is discussed. The first order of accuracy difference scheme for elliptic nonlocal identification problem is studied. By using spectral resolution of a self-adjoint operator, we establish stability inequalities for solution of constructed scheme. Subsequently, the difference scheme for approximate solution of multidimensional boundary value problem with integral-type nonlocal and first kind boundary conditions is investigated on stability. Numerical test examples are presented.     

Lower and upper bounds of large deviation for sums of subexponential claims in a multi-risk model

In view of the actual condition of the insurance company, a multi-risk model is proposed. The lower and upper bounds for the sums of subexponential claims in this model are given. The proof method is based on the results of the total claim amount under subexponential class.     

V-uniform ergodicity of a continuous time asymmetric power GARCH(1,1) model

A continuous time asymmetric power GARCH(1,1) model is presented and the V-uniform ergodicity and β-mixing property of the process with exponential decay rate are proved. The V-uniform ergodicity of the COGARCH(1,1) model is obtained as a special case.     

Tail asymptotics for the queue length in an M/G/1 retrial queue

In this paper, we study the tail behavior of the stationary queue length of an M/G/1 retrial queue. We show that the subexponential tail of the stationary queue length of an M/G/1 retrial queue is determined by that of the corresponding M/G/1 queue, and hence the stationary queue length in an M/G/1 retrial queue is subexponential if the stationary queue length in the corresponding M/G/1 queue is subexponential. Our results for subexponential tails also apply to regularly varying tails, and we provide the regularly varying tail asymptotics for the stationary queue length of the M/G/1 retrial queue. AMS subject classifications: 60J25, 60K25     

Strong Law of Large Numbers and Central Limit Theorems for Functionals of Inhomogeneous Semi-Markov Processes

Limit theorems for functionals of classical (homogeneous) Markov renewal and semi-Markov processes have been known for a long time, since the pioneering work of Pyke Schaufele (Limit theorems for Markov renewal processes, Ann. Math. Statist., 35(4):1746–1764, 1964). Since then, these processes, as well as their time-inhomogeneous generalizations, have found many applications, for example, in finance and insurance. Unfortunately, no limit theorems have been obtained for functionals of inhomogeneous Markov renewal and semi-Markov processes as of today, to the best of the authors’ knowledge. In this article, we provide strong law of large numbers and central limit theorem results for such processes. In particular, we make an important connection of our results with the theory of ergodicity of inhomogeneous Markov chains. Finally, we provide an application to risk processes used in insurance by considering a inhomogeneous semi-Markov version of the well-known continuous-time Markov chain model, widely used in the literature.     

Conditional distribution of heavy tailed random variables on large deviations of their sum

It is known that large deviations of sums of subexponential random variables are most likely realised by deviations of a single random variable. In this article we give a detailed picture of how subexponential random variables are distributed when a large deviation of the sum is observed.     

关于局部次指数分布的一个注记

通过次指数密度函数建立了局部次指数分布类的一个等价刻画.作为其应用,我们证明了局部次指数分布类不具有卷积封闭性.     

SEM Modeling with Singular Moment Matrices Part II: ML-Estimation of Sampled Stochastic Differential Equations

Linear stochastic differential equations are expressed as an exact discrete model (EDM) and estimated with structural equation models (SEMs) and the Kalman filter (KF) algorithm. The oversampling approach is introduced in order to formulate the EDM on a time grid which is finer than the sampling intervals. This leads to a simple computation of the nonlinear parameter functionals of the EDM. For small discretization intervals, the functionals can be linearized, and standard software permitting only linear parameter restrictions can be used. However, in this case the SEM approach must handle large matrices leading to degraded performance and possible numerical problems. The methods are compared using coupled linear random oscillators with time-varying parameters and irregular sampling times.     

Second order tail behaviour for heavy-tailed sums and their maxima with applications to ruin theory

In this paper we establish the second order asymptotics for the tail probabilities of partial sums of independent real random variables and the maxima of these sums under the framework of subexponential distributions. For this aim, second order subexponential distributions are extended to the whole real line. An application to ruin theory is involved.