Inverse problem for a hyperbolic equation with nonlocal boundary condition containing a delay argument

We investigate a multitype Galton-Watson process in a random environment generated by a sequence of independent identically distributed random variables. Assuming that the mean of the increment X of the associated random walk constructed by the logarithms of the Perron roots of the reproduction mean matrices is negative and the random variable Xe ^X has zero mean, we find the asymptotics of the survival probability at time n as n → ∞.     

Stabilization of statistics in wave and Klein-Gordon equations with mixing. Scattering theory for infinite energy solutions

We consider wave and Klein-Gordon equations in the whole space ?ⁿ with arbitraryn≥2. We assume initial data to be homogeneous random functions in ?ⁿ with zero expectation and finite mean density of energy. Moreover, we assume initial data fit mixing condition of Ibragimov-Linnik type. We consider the distributions of the random solution at the moment of timet. The main results mean the convergence of this distribution to some Gaussian measure ast→∞. This is a central limit theorem for wave and Klein-Gordon equations. The limit Gaussian measures are invariant measures for equations considered. Corresponding stationary random solutions are ergodic and mixing in time. The results are inspired by mathematical problems of statistical physics.     

一类随机游动上确界的密度的渐近性

Kluppelberg^[1], Asmussen 等^[2] 研究了增量有有限负均值的随机游动上确界的密度的渐近性. 该文则在 Denisov 等^[3], 程东亚和王岳宝^[4]的基础上, 进一步研究了增量均值为负无穷的随机游动上确界的密度的渐近性. 最后, 为了说明常见重尾分布大多满足上述结果的条件, 该文给出了一些分布族的性质.     

Analysis of a Discrete-Time Finite-Capacity Single-Server Queue with Markovian-Arrival Process and Random-Bulk-Service: D-MAP/G Y /1/M

In this article, we consider a single-server, finite-capacity queue with random bulk service rule where customers arrive according to a discrete-time Markovian arrival process (D-MAP). The model is denoted by D-MAP/G ^Y /1/M where server capacity (bulk size for service) is determined by a random variable Y at the starting point of services. A simple analysis of this model is given using the embedded Markov chain technique and the concept of the mean sojourn time of the phase of underlying Markov chain of D-MAP. A complete solution to the distribution of the number of customers in the D-MAP/G ^Y /1/M queue, some computational results, and performance measures such as the average number of customers in the queue and the loss probability are presented.     

一类对称多项式在微分几何中的应用

本文研究了卵形面特征刻画.利用麦克劳林不等式及对称多项式的性质,获得了一个An+1中的卵形面,若其任意三个连续高阶仿射平均曲率乘积为常熟,且Ln=0,则该卵形面为椭圆的结果.推广了现有文献关于卵形面的刻画结果.     

Metastability of Nonreversible Random Walks in a Potential Field and the Eyring‐Kramers Transition Rate Formula

We consider nonreversible random walks in a bounded domain of ℝ^d evolving on a potential field. We describe the complete metastable behavior of the random walk among the landscape of valleys, and we derive the Eyring‐Kramers formula for the mean transition time from a metastable set to a stable set.© 2017 Wiley Periodicals, Inc.     

Conditional limiting distribution of Type III elliptical random vectors

In this paper we consider elliptical random vectors in R^d,d≥2 with stochastic representation RAU where R is a positive random radius independent of the random vector U which is uniformly distributed on the unit sphere of R^d and A∈R^d×d is a non-singular matrix. When R has distribution function in the Weibull max-domain of attraction we say that the corresponding elliptical random vector is of Type III. For the bivariate set-up, Berman [Sojurns and Extremes of Stochastic Processes, Wadsworth & Brooks/ Cole, 1992] obtained for Type III elliptical random vectors an interesting asymptotic approximation by conditioning on one component. In this paper we extend Berman's result to Type III elliptical random vectors in R^d. Further, we derive an asymptotic approximation for the conditional distribution of such random vectors.     

A fuzzy bootstrap test for the mean with <Emphasis Type="Italic">D</Emphasis><Subscript><Emphasis Type="Italic">p,q</Emphasis></Subscript>-distance

In this paper, we consider the problem of testing a simple hypothesis about the mean of a fuzzy random variable. For this purpose, we take a distance between the sample mean and the mean in the null hypothesis as a test statistic. An asymptotic test about the fuzzy mean is obtained by using a central limit theorem. The asymptotical distribution is ω ₂-distribution. The ω ₂-distribution is only known for special cases, thus we have considered random LR-fuzzy numbers. In the fuzzy concept, in addition to the existence of several versions of the central limit theorem, there is another practical disadvantage: The limit law is, in most cases, difficult to handle. Therefore, the central limit theorem for fuzzy random variable does not seem to be a very useful tool to make inferences on the mean of fuzzy random variable. Thus we use the bootstrap technique. Finally, by means of a simulation study, we show that the bootstrap method is a powerful tool in the statistical hypothesis testing about the mean of fuzzy random variables.     

Testing Epidemic Changes of Infinite Dimensional Parameters

To detect epidemic change in the mean of a sample of size n of random elements in a Banach space, we introduce new test statistics DI based on weighted increments of partial sums. We obtain their limit distributions under the null hypothesis of no change in the mean. Under alternative hypothesis our statistics can detect very short epidemics of length log^γ n, γ > 1. We present applications to detect epidemic changes in distribution function or characteristic function of real valued observations as well as changes in covariance matrices of random vectors. Final version 27 October 2004     

Measurability of inverses of random operators and existence theorems

Let (Ω,B,μ) be ameasure space andX a separable Hubert space. LetT be a random operator from Ω ×X intoX. In this paper we investigate the measurability ofT ^-1. In our main theorems we show that ifT is a separable random operator withT(w) almost sure invertible and monotone and demicontinuous thenT ^-1is also a random operator. As an application of this we give an existence theorem for random Hammerstein operator equation.     

von Neumann��s mean ergodic theorem on complete random inner product modules

We first prove two forms of von Neumann’s mean ergodic theorems under the framework of complete random inner product modules. As applications, we obtain two conditional mean ergodic convergence theorems for random isometric operators which are defined on L _ℱ ^p (ℰ, H) and generated by measure-preserving transformations on Ω, where H is a Hilbert space, L ^p (ℰ, H) (1 ⩽ p < ∞) the Banach space of equivalence classes of H-valued p-integrable random variables defined on a probability space (Ω, ℰ, P), F a sub σ-algebra of ℰ, and L _ℱ ^p (ℰ(E,H) the complete random normed module generated by L ^p (ℰ, H).     

Random weights, robust lattice rules and the geometry of the cbcrc algorithm

In this paper we study lattice rules which are cubature formulae to approximate integrands over the unit cube [0,1] ^s from a weighted reproducing kernel Hilbert space. We assume that the weights are independent random variables with a given mean and variance for two reasons stemming from practical applications: (i) It is usually not known in practice how to choose the weights. Thus by assuming that the weights are random variables, we obtain robust constructions (with respect to the weights) of lattice rules. This, to some extend, removes the necessity to carefully choose the weights. (ii) In practice it is convenient to use the same lattice rule for many different integrands. The best choice of weights for each integrand may vary to some degree, hence considering the weights random variables does justice to how lattice rules are used in applications. In this paper the worst-case error is therefore a random variable depending on random weights. We show how one can construct lattice rules which perform well for weights taken from a set with large measure. Such lattice rules are therefore robust with respect to certain changes in the weights. The construction algorithm uses the component-by-component (cbc) idea based on two criteria, one using the mean of the worst case error and the second criterion using a bound on the variance of the worst-case error. We call the new algorithm the cbc2c (component-by-component with 2 constraints) algorithm. We also study a generalized version which uses r constraints which we call the cbcrc (component-by-component with r constraints) algorithm. We show that lattice rules generated by the cbcrc algorithm simultaneously work well for all weights in a subspace spanned by the chosen weights ?? ⁽¹⁾, . . . , ?? ^(r). Thus, in applications, instead of finding one set of weights, it is enough to find a convex polytope in which the optimal weights lie. The price for this method is a factor r in the upper bound on the error and in the construction cost of the lattice rule. Thus the burden of determining one set of weights very precisely can be shifted to the construction of good lattice rules. Numerical results indicate the benefit of using the cbc2c algorithm for certain choices of weights.     

The continuum limit of critical random graphs

We consider the Erd?s–Rényi random graph G(n, p) inside the critical window, that is when p?=?1/n?+?λn ^?4/3, for some fixed ${\lambda \in \mathbb{R}}$ . We prove that the sequence of connected components of G(n, p), considered as metric spaces using the graph distance rescaled by n ^?1/3, converges towards a sequence of continuous compact metric spaces. The result relies on a bijection between graphs and certain marked random walks, and the theory of continuum random trees. Our result gives access to the answers to a great many questions about distances in critical random graphs. In particular, we deduce that the diameter of G(n, p) rescaled by n ^?1/3 converges in distribution to an absolutely continuous random variable with finite mean.     

Relations between some basic results derived from two kinds of topologies for a random locally convex module

The purpose of this paper is to exhibit the relations between some basic results derived from the two kinds of topologies (namely the (ε,λ)-topology and the stronger locally L⁰-convex topology) for a random locally convex module. First, we give an extremely simple proof of the known Hahn-Banach extension theorem for L⁰-linear functions as well as its continuous variant. Then we give the relations between the hyperplane separation theorems in [D. Filipovi?, M. Kupper, N. Vogelpoth, Separation and duality in locally L⁰-convex modules, J. Funct. Anal. 256 (2009) 3996-4029] and a basic strict separation theorem in [T.X. Guo, H.X. Xiao, X.X. Chen, A basic strict separation theorem in random locally convex modules, Nonlinear Anal. 71 (2009) 3794-3804]: in the process we also obtain a very useful fact that a random locally convex module with the countable concatenation property must have the same completeness under the two topologies. As applications of the fact, we prove that most of the previously established principal results of random conjugate spaces of random normed modules under the (ε,λ)-topology are still valid under the locally L⁰-convex topology, which considerably enriches financial applications of random normed modules.     

A Note on a Composition of Two Random Integral Mappings β and Some Examples

Abstract

The method of random integral representation, that is, the method of representing a given probability measure as the probability distribution of some random integral, was quite successful in the past few decades. In this note, we show that a composition of two random integral mappings ^β is again a random integral mapping. We illustrate our results with some examples.     

On bounds for bulk arrival queues

This paper gives a simple and effective approach pf deriving bounds for bulk arrival queues by making use of the bounds for single arrival queues. With this approach, upper bounds of mean actual/virtual waiting times and mean queue length at random epochs can be derived for the bulk arrival queues GI^X/G/1 and GI^X/G/c (lower bounds can be derived in a similar way). The merit of this approach is shown by comparing the bounds obtained with some existing results in the literature.     

The hitting distributions of a half real line for two-dimensional random walks

For every two-dimensional random walk on the square lattice Z ² having zero mean and finite variance we obtain fine asymptotic estimates of the probability that the walk hits the negative real line for the first time at a site (s,0), when it is started at a site far from both (0,s) and the origin.     

Random fixed point theorems for composites of acyclic multifunctions

In this paper we obtain random versions of Kakutani–Fan type fixed point theorems for a class V _c ⁺ of multifunctions which contains Kakutani factorizable maps and composites of acyclic maps. As applications, we derive some random approximation theorems.     

Random periodic solutions of random dynamical systems

In this paper, we give the definition of the random periodic solutions of random dynamical systems. We prove the existence of such periodic solutions for a C¹ perfect cocycle on a cylinder using a random invariant set, the Lyapunov exponents and the pullback of the cocycle.