Approximation Properties of a Special Class of Mathematical Expectation Operators

61-IntroductionLet(X.}"cNbeasequenceofindependentrandomvariableseachhavingthesamelatticepointdistributionwithprobabilityfunctionP(X,=a kh)=P*,expectationEX"=),l(x)andvarianceE(X"-ax")'=a2(x).WhereKeZ:={o,tl,l2,..'},a,harethepositivecon-stants,xeI=Y'=Ri8arealcontinuousparameter.LettheprobabilitydistributionofS,=ZX,beForacontinuousfunctionfontheinterval7'(possiblyinfinite)definethemathematicalex-pectationoperatorRemarks(l)UsingChebychev,sinequalitywegeteasily.(See[1,P,,,f,,.j)-(2)Manyo…     

Needle Sharing Infections among Heterogeneous IVDUS

 This paper begins with an alternative derivation of the coefficients in a known probability generating function (pgf ), namely that for the number of new infectives generated in a random allocation model of needle sharing among i infectives and n susceptibles. The expectation and variance of the number of new infectives are derived. The pgf for such a model is then obtained when there are types of susceptibles; the probabilities of generating new infectives are found for , where the infectives have preferential probabilities p and q for type 1 and 2 susceptibles respectively. The case of variable susceptibilities is also considered, and the paper concludes with some remarks on the pgf method. Received 21 February 2001; in final form 15 September 2001     

Bilevel programming and the separation problem

In recent years, branch-and-cut algorithms have become firmly established as the most effective method for solving generic mixed integer linear programs (MILPs). Methods for automatically generating inequalities valid for the convex hull of solutions to such MILPs are a critical element of branch-and-cut. This paper examines the nature of the so-called separation problem, which is that of generating a valid inequality violated by a given real vector, usually arising as the solution to a relaxation of the original problem. We show that the problem of generating a maximally violated valid inequality often has a natural interpretation as a bilevel program. In some cases, this bilevel program can be easily reformulated as a simple single-level mathematical program, yielding a standard mathematical programming formulation for the separation problem. In other cases, no such polynomial-size single-level reformulation exists unless the polynomial hierarchy collapses to its first level (an event considered extremely unlikely in computational complexity theory). We illustrate our insights by considering the separation problem for two well-known classes of valid inequalities.     

Variable sample size method for equality constrained optimization problems

An equality constrained optimization problem with a deterministic objective function and constraints in the form of mathematical expectation is considered. The constraints are transformed into the Sample Average Approximation form resulting in deterministic problem. A method which combines a variable sample size procedure with line search is applied to a penalty reformulation. The method generates a sequence that converges towards first-order critical points. The final stage of the optimization procedure employs the full sample and the SAA problem is eventually solved with significantly smaller cost. Preliminary numerical results show that the proposed method can produce significant savings compared to SAA method and some heuristic sample update counterparts while generating a solution of the same quality.     

Schur-Weyl duality and the heat kernel measure on the unitary group

We investigate a relation between the Brownian motion on the unitary group and the most natural random walk on the symmetric group, based on Schur-Weyl duality. We use this relation to establish a convergent power series expansion for the expectation of a product of traces of powers of a random unitary matrix under the heat kernel measure. This expectation turns out to be the generating series of certain paths in the Cayley graph of the symmetric group. Using our expansion, we recover asymptotic results of Xu, Biane and Voiculescu. We give an interpretation of our main expansion in terms of random ramified coverings of a disk.     

Characteristic operator and the curvilinear integral for a semi-Markov process

The connection between the characteristic operator and the Lévy representation of the conditional generating function of the first exit time of a semi-Markov process is considered. The absolutely continuous part of Lévy's additive functional is expressed in the form of a curvilinear integral of the value of the characteristic operator of unity with respect to the conditional mathematical expectation of the traversal time relative to sequences of states. The obtained formula is used for a new derivation of the linearity of the characteristic operator for a Markov process.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademii Nauk SSSR, Vol. 177, pp. 170–180, 1989.     

正态总体均值置信区间长度的比较

当单个正态总体方差分别为已知和未知时,总体均值置信区间的长度比较问题仍待探讨.利用样本标准差数学期望的性质,通过积分变换的方法证明了前者小于后者的期望.     

Band-times-circulant preconditioners for non-symmetric Toeplitz systems

BIT Numerical Mathematics - In this paper we study $$n\times n$$ non-symmetric, real Toeplitz systems of the form $$T_n(f)x = b$$ , where the generating function of the Toeplitz matrix f is known a...     

On the existence of values for arbitration games

Two-person games in normal form are considered, where the players may use correlated strategies and where the problem arises, which Pareto optimal point in the payoff region to choose. We suppose that the players solve this problem with the aid of an arbitration function, which is continuous and profitable, and for which the inverse image of each Pareto point is a convex set. Then the existence of values and defensive ε-optimal strategies is discussed. Existence theorems are derived, using families of suitable dummy zero-sum games. The derived existence theorems contain all known existence results as special cases.     

Properties of minimal mathematical expectations

The aim of this paper is to discuss how to compute a class of minimal mathematical expectations by using backward stochastic differential equations. We also prove that the minimal mathematical expectation operator still preserves some properties of the mathematical expectation operator.     

Phase-type distribution of customer relationship with Markovian response and marketing expenditure decision on the customer lifetime value

In recent years, more and more companies have adopted relationship marketing (RM). At the core of RM is the development and maintenance of long-term relationships with valuable customers. In RM, the customer lifetime value (CLV) is the discounted profit streams of a customer across the entire customer life cycle. The CLV plays a key role in customer acquisition and retention decisions. In this paper, we present a general mathematical framework for RM, and introduce a Markov chain model which is appropriate in modeling RM because of its flexibility and probabilistic nature. We also develop the life distribution of the customer relationship, which is a phase-type distribution since it is the distribution of the first arrival stopping state. And we obtain the expectation of the CLV, which is an important statistic for good decision-making. Finally, we illustrate how to find the optimal remarketing policy numerically. The framework developed for RM systems in this paper should be seen as a practical approach to RM where one can directly apply the results of phase-type distribution and expectation of CLV to marketing decisions.     

Classification of locally rotationally symmetric Bianchi-I space–times using conformal Ricci collineations

We present a complete classification of locally rotationally symmetric (LRS) Bianchi-I space–times in accordance with their conformal Ricci collineations (CRCs). In the case where the Ricci tensor is nondegenerate, we find a general form of the vector field generating CRCs subject to some integrability conditions. Solving the integrability conditions in different cases, we find that the LRS Bianchi-I space–times admit 7-, 10-, 11-, or 15-dimensional Lie algebras of CRCs in the case where the Ricci tensor is nondegenerate. Moreover, we find that these space–times admit an infinite number of CRCs if the Ricci tensor is degenerate. We give some examples of LRS Bianchi-I space–times that admit nontrivial CRCs and are models of a perfect fluid.     

Families of m-convex polygons:

Polygons are described as almost-convex if their perimeter differs from the perimeter of their minimum bounding rectangle by twice their ‘concavity index’, m. Such polygons are called m-convex polygons. We first use the inclusion–exclusion principle to rederive the known generating function for 1-convex self-avoiding polygons (SAPs). We then use our results to derive the exact anisotropic generating functions for osculating and neighbour-avoiding 1-convex SAPs, their isotropic form having recently been conjectured.     

Jump-type processes and their applications in quantum mechanics

A survey is presented of mathematical methods in the theory of the Feynman path integral. Principal attention is devoted to new results making it possible to represent the solution of the Cauchy problem for the Schrödinger equation and a quasilinear equation of Hartree type in the form of the mathematical expectation of functionals on jump-type Markov processes and to use Monte Carlo methods for solving these equations. A brief survey of results on complex Markov chains is presented.Translated from Itogi Nauki i Tekhniki. Teoriya Veroyatnostei, Matematicheskaya Statistika, Teoreticheskaya Kibernetika, Vol. 15, pp. 5–78, 1978.     

Market frictions and corporate finance: an overview paper

We present an overview of corporate-finance models where firms are subject to exogenous market frictions. These models, albeit quite simple, yield reasonable predictions regarding financing, pay-outs and default, as well as asset-pricing implications. The price to pay for the said simplicity is the need to use non-standard mathematical techniques, namely singular and impulse stochastic control. We explore the cases where a firm with fixed expected profitability has access to costly equity issuance as a refinancing possibility, and that where issuance is infinitely costly. We also present a model of bank leverage.     

绝对破产下具有贷款利息及常数分红界的扰动复合Poisson风险模型

该文研究了绝对破产下具有贷款利息及常数分红界的扰动复合Poisson风险模型,得到了折现分红总量的均值函数,及其矩母函数以及此模型的期望折现罚金函数(Gerber-Shiu函数)满足的积分-微分方程及边值条件,并求出了某些特殊情形下的具体表达式.     

A simplified proof of the Doob-Meyer theorem for nonnegative submartingales

An elementary proof of a representation of a nonnegative submartingale in the form of a conditional mathematical expectation of an increasing stochastic process is given. Using this representation, a simplified proof of a decomposition of a positive submartingale into the sum of a martingale and an increasing natural process is provided.     

The language of geodesics for Garside groups

We prove that the language of all geodesics of any Garside group, with respect to the generating set of divisors of the Garside element, forms a regular language. In particular, the braid groups admit generating sets where the associated language of geodesics is regular.in final form: 28 October 2003Charney was partially supported by NSF grant DMS-0104026. Meier thanks the AMS for the support of a Centennial Research Fellowship.     

There are Infinitely Many Williams Squares with Circular Structure and Order a Multiple of 4

Williams squares, also known as row quasi-complete Latin squares, that have circular structure are used in repeated measurements designs where error terms are correlated. They are known to exist for all orders that are not multiples of 4 and also order 8; there is no such square of order 4. We use a variation of the generating array method to construct a Williams square of order 12 with circular structure. We also give a product theorem that produces Williams squares of orders 8r and 12s, where the smallest prime divisor of r is at least 11 and the smallest prime divisor of s is at least 13, that have circular structure.     

Mathematical Modelling of Diesel-Electric Propulsion Systems for Marine Vessels

This article presents a mathematical model of a complete diesel-electric propulsion system, including components as diesel generators, distribution network, variable speed thruster-drives, and conventional motor loads. The model is split into two parts: One power generating part where the load is specified with an aggregated active and reactive power load demand. Secondly, a power consumption part where the effects of the different load types as thruster drives, motors and other loads are modelled. The model is written in a state-space form suitable for the purpose of simulation and control design. PID-controllers represent speed governors and automatic voltage regulators.