bluuebunny/crossref_metadata_2025 huggingface dataset:
What is good journalism? comparing Israeli public and journalists' perspectives
Authors: Tsfati Yariv , Meyers Oren , Peri Yoram
Published: April 2006

The frequent referencing of service to the public interest as a core professional journalistic value raises the question of the correspondence between the perception of journalists and the public as to what constitutes good and bad journalism. In this study, a sample of Israeli journalists and a sample of the Israeli public were asked a series of questions about the core values and practices of journalism. Results suggest four major conclusions: first, Israeli journalists have a clear, relatively uniform perception of what constitutes worthy journalism. Second, journalists and the public differ in the degrees of significance they assign to various journalistic norms and practices. Third, the public is slightly more positive in its overall assessment of the Israeli media in comparison with the journalists. Finally, the two general assessments are constituted by different, or even opposing, components.
Differential action of steroid hormones on human endothelium
Authors: Oberleithner Hans , Riethmüller Christoph , Ludwig Thomas , Shahin Victor , Stock Christian , Schwab Albrecht , Hausberg Martin , Kusche Kristina , Schillers Hermann
Published: April 2006

The action of glucocorticoids on vascular permeability is well established. However, little is known about the action of mineralocorticoids on the structure and function of blood vessels. As endothelial cells are targets for both glucocorticoids and mineralocorticoids, we exposed human umbilical vein endothelial cells to both types of steroids. Aldosterone (mineralocorticoid) and dexamethasone (glucocorticoid) were applied for 3 days in culture before measurements of transendothelial ion and macromolecule permeability, apical cell surface and cell stiffness were taken. Transendothelial ion permeability was measured with electrical cell impedance sensing, macromolecule permeability with fluorescence-labeled dextran and apical cell membrane surface by three-dimensional AFM imaging. Cell stiffness was measured using the AFM scanning tip as a mechanical nanosensor. We found that aldosterone increased both apical cell surface and apical cell stiffness significantly, while transendothelial permeability remained unaffected. By contrast, dexamethasone significantly decreased ion and macromolecule permeability, while apical cell surface and cell stiffness did not change. Specific receptor antagonists for dexamethasone (RU486) and aldosterone (spironolactone) prevented the observed responses. We conclude that glucocorticoids strengthen cell-to-cell contacts (`peripheral action'), whereas mineralocorticoids enlarge and stiffen cells (`central action'). This could explain the dexamethasone-mediated retention of fluid in the vascular system, and endothelial dysfunction in states of hyperaldosteronism.
Measuring aggregate human capital in Portugal: 19602001
Authors: Teixeira Aurora Amlia Castro
Published: April 2006

Recent studies conclude that human capital should be a high priority because it is a key growth input, particularly in an increasingly knowledge-based economy and an important lever of social cohesion policy. However, country-specific studies involving human capital and economic performance
are scarce both for Portugal and for other countries. The small number of such studies is explained to a large extent by the increased complexity and difficulty of estimating continuous time series for human capital stock giving data paucity. This article tries to facilitate the emergence
of further empirical works on the relation between human capital and long-term economic growth by providing an improved measure of the stock of human capital for the Portuguese economy from 1960 up to 2001.
On a stochastic integral equation of the Volterra type in telephone traffic theory
Authors: Padgett W. J. , Tsokos C. P.
Published: April 2006

In mathematical models of phenomena occurring in the general areas of the engineering, biological, and physical sciences, random or stochastic equations appear frequently. In this paper we shall formulate a problem in telephone traffic theory which leads to a stochastic integral equation which is a special case of the Volterra type of the form

where:

(i)

ω∊Ω, where Ω is the supporting set of the probability measure space (Ω,B,P);

(ii)

x(t; ω) is the unknown random variable for t ∊ R+, where R+ = [0, ∞);

(iii)

y(t; ω) is the stochastic free term or free random variable for t ∊ R+;

(iv)

k(t, τ; ω) is the stochastic kernel, defined for 0 ≦ τ ≦ t < ∞; and

(v)

f(t, x) is a scalar function defined for t ∊ R+ and x ∊ R, where R is the real line.
On large sample sequential analysis with applications to survivorship data
Authors: Breslow Norman
Published: April 2006

Although his work on the application of invariance concepts to the sequential testing of composite hypotheses is better known, Cox (1963) has also outlined a large sample approach to the same problem. His method is based on Bartlett's (1946) recognition that the sequence of maximum likelihood estimates (MLE) of the parameter of interest, calculated from an increasing number of observations, resembles asymptotically a random walk of normally distributed variables. However, the large sample theory needed to justify this approach rigorously is left largely implicit. At the end of his paper, Cox suggests that these methods may be extended to yield a sequential comparison of survival curves (Armitage (1959)), a suggestion which has been reiterated as a research problem in the monograph of Wetherill (1966).
On two integral equations of queueing theory
Authors: Cohen J. W.
Published: April 2006

In the present paper the solutions of two integral equations are derived. One of the integral equations dominates the mathematical description of the stochastic process {vn, n = 1,2, …}, recursively defined by
K is a positive constant, τ1, τ2, …; Σ1, Σ2, …; are independent, non-negative variables, with τ1, τ2,…, identically distributed, similarly, the variables Σ1, Σ2, …, are identically distributed.
On the converse to the iterated logarithm law
Authors: Heyde C. C.
Published: April 2006

Let Xi, i = 1, 2, 3,… be a sequence of independent and identically distributed random variables with law ℓ(X) and write. if EX= 0 and EX2=σ2< ∞, the law of the iterated logarithm (Hartman and Wintner [1]) tells us that
Embedding submartingales in wiener processes with drift, with applications to sequential analysis
Authors: Hall W. J.
Published: April 2006

Skorokhod (1961) demonstrated how the study of martingale sequences (and zero-mean random walks) can be reduced to the study of the Wiener process (without drift) at a sequence of random stopping times. We show how the study of certain submartingale sequences, including certain random walks with drift and log likelihood ratio sequences, can be reduced to the study of the Wiener process with drift at a sequence of stopping times (Theorem 4.1). Applications to absorption problems are given. Specifically, we present new derivations of a number of the basic approximations and inequalities of classical sequential analysis, and some variations on them — including an improvement on Wald's lower bound for the expected sample size function (Corollary 7.5).
Optimal dispatching of a poisson process
Authors: Ross Sheldon M.
Published: April 2006

Items arrive at a processing plant at a Poisson rate λ. At time T, all items are dispatched from the system. An intermediate dispatch time is to be chosen to minimize the total wait of all items. It is shown that if the dispatch time must be chosen at time 0 then T/2 not only minimizes the expected total wait but it also maximizes the probability that the total wait is less than a for every a > 0. If the intermediate dispatch time is allowed to be a (random) stopping time, then it is shown that the policy which dispatches at time t iff N(t) > λ(T – t) is optimal, where N(t) denotes the number of items present at time t. The distribution of the optimal dispatch time and the optimal expected total wait are determined. A generalization to the case of a non-homogeneous Poisson process, a time lag, and batch arrivals is given. Finally, the case where the process goes on indefinitely and any number of dispatches are allowed (at a cost K per dispatch) is considered.
Bunching in a semi-Markov process
Authors: Hawkes A. G.
Published: April 2006

In the type II counter with constant deadtime, particles which arrive within some constant time τ following another particle are unrecorded. We can think of this process as an alternating sequence of gaps and bunches of events. Gaps have duration > τ, while the intervals between any successive pair of events within a bunch are all ≦ τ. Counter theory is usually concerned with the distribution of intervals between recorded events (i.e., the first event of each bunch) and the distribution of the number of recorded events in a given time interval. In the case where the events form a renewal process this has been studied intensively by Pyke [2], Smith [5] and Takács [6].
On random genetic drift in a subdivided population
Authors: Pollak Edward
Published: April 2006

Generations are assumed to be non-overlapping. We consider a haploid population divided intoKparts, each of which containNadults in any generation. These are obtained by a random sampling of the offspring of the previous generation. We assume that the probability of an adult offspring of an individual in one subpopulation being in some other subpopulation is the same small positive number, no matter what two subpopulations are considered.

If the population initially has individuals of two types, A and a, it is of interest to study approximations, if n is large, to

(1)

the rate at which A or a is lost between generations n-1 and n,

(2)

the probability that A and a are still present in generation n,

(3)

the joint distribution of frequencies of A in the subpopulations.

A solution is given for the first problem. It is found that if the mean number of migrants per generation from one subpopulation to another is at least as large as 1, the population behaves almost as if it were not subdivided. But if this number is considerably less that 1, then the rate at which one or the other gene is lost is slower than in an undivided population. The other two problems are discussed for K = 2.
On the existence of the expectation of randomly stopped sums
Authors: Samuel Ester
Published: April 2006

Let a+ = a if a > 0, a+ = 0 otherwise, and a– = (– a)+.
Traffic light queues with dependent arrivals as a generalization to queueing theory
Authors: Ohno Katsuhisa , Mine Hisashi
Published: April 2006

This paper considers a fixed-cycle and a semi vehicular-actuated traffic light queue with strictly stationary arrivals and independent and identically distributed departure headways and lost times. These queues are reduced to a generalized model of Loynes and sufficient conditions are derived under which these queues have stationary distributions. Two typical examples of semi vehicular-actuated traffic light queues are discussed.
Non-stationary random set processes with application to pattern reconstruction
Authors: Moore Marc
Published: April 2006

Examples of non-stationary random set processes are presented. The reconstruction of a pattern, generated by such a process, is studied; a particular arrangement of the sample-points is considered.
An extension of Erlang's loss formula
Authors: Wolff Ronald W. , Wrightson Charles W.
Published: April 2006

A two-server loss system is considered with N classes of Poisson arrivals, where the service distribution function and server preferences are arrival-class dependent. The stationary state probabilities are derived and found to be independent of the form of the service distributions.
On a theorem of Ahsanullah and Rahman
Authors: Huang J. S.
Published: April 2006

A characterization theorem of the exponential distribution by Ahsanullah and Rahman is examined in contrast to existing results by several other authors.
Bounds for the extinction probability of a simple branching process
Authors: Quine M. P.
Published: April 2006

The extinction probability q of a supercritical simple branching process is well known to be less than unity. Intuitively, it is apparent that when the offspring mean is close to one, so, usually, will q be. This notion is made rigorous, and simple bounds are given for q in terms of the second and third factorial moments, which are applicable when the offspring mean is close to unity. A comparison is made of various upper bounds for q. The note contains some numerical examples.
The joint probability density function of the occupation time of a three-state problem
Authors: Hsia Wei Shen
Published: April 2006

The joint probability density function of the occupation time of a three-state stochastic process with constant transition matrix: aij ≠ 0, i ≠ j, i, j = 1, 2, 3 but αii = 0, i = 1, 2, 3 is studied.
Inequalities with application in retail inventory analysis
Authors: Agnew Robert A.
Published: April 2006

Simple bounds on service level and turnover velocity are obtained for a periodic-review inventory system with a stationary order-up-to-level stocking policy and no backordering. Exact computational formulas are given for Poisson demand. An illustrative numerical example is presented, and the application of these bounds to retail inventory analysis is discussed.
Record values and inter-record times
Authors: Shorrock R. W.
Published: April 2006

First, asymptotic results for inter-record times when the CDF of the underlying IID process is not necessarily continuous are obtained, by a stochastic order argument, from known results for the continuous case. Then the asymptotic behaviour of the bivariate process of upper-record values and inter-record times is studied. Finally, assuming continuity of the underlying CDF, we derive the law of the process of total times spent in sets of states, viewing upper record values as states and inter-record times as times spent in a state, the process so viewed being a discrete time continuous state Markov jump process.

The possible relevance of this result to single lane road traffic flow is indicated.
A convergence theorem for parities in a birth-and-death process
Authors: Saunders I. W.
Published: April 2006

The parity of an individual in a population process is the number of offspring that individual has produced. If Nk(t) is the number of individuals of parity k at time t in a birth-and-death process and we show that, conditional on N(t)→ ∞,
A functional equation and its application to the characterization of the Weibull and stable distributions
Authors: Wang Y. H.
Published: April 2006

The Cauchy functional equation Φ(x + y) = Φ(x) + Φ(y) is generalized to the form , assuming Φ is left- or right- continuous. This result is used to obtain (1) a characterization of the Weibull distribution, in the spirit of the memoryless property of the exponential distribution, by , for all x, y ≧ 0;(2) a characterization of the symmetric α-stable distribution by the equidistribution of linear statistics.
On a multivariate generalized occupancy model
Authors: Johnson N. L. , Kotz Samuel
Published: April 2006

A generalized occupancy distribution obtained by Uppuluri and Carpenter (1971) is derived by elementary methods, and extended to a multivariate situation.
A simple random walk on parallel axes moving at different rates
Authors: Barnett V.
Published: April 2006

Prompted by a rivulet model for the flow of liquid through packed columns we consider a simple random walk on parallel axes moving at different rates. A particle may make one of three transitions at each time instant: to the right or to the left on the axis it was on at the previous time instant, or across to the other axis. Results are obtained for the unrestricted walk, and for the walk with absorbing, or reflecting, end-points.
The discrete asymptotic behaviour of a simple batch epidemic process
Authors: Billard L. , Lacayo H. , Langberg N. A.
Published: April 2006

A simple epidemic process in which the number of individuals who can become infected at any point in time is itself a random variable is described. The discrete asymptotic behaviour of such a process is discussed. In particular, the associated marginal distribution of the limiting process is considered.
Percolation on subsets of the square lattice
Authors: McDiarmid Colin
Published: April 2006

We adapt arguments from a paper of Seymour and Welsh concerning percolation probabilities on the infinite square lattice L to show that for certain regions R in L, if there is a positive probability of having an infinite open path in L starting at the origin then there is also a positive probability of having such a path within R.
Imbedded and non-imbedded stationary characteristics of queueing systems with varying service rate and point processes
Authors: König D. , Schmidt V.
Published: April 2006

In this paper a unified approach is used for proving relationships between customer-stationary and time-stationary characteristics of service systems with varying service rate and point processes. This approach is based on an intensity conservation principle for general stationary continuous-time processes with imbedded stationary marked point processes. It enables us to work under weaker independence assumptions than usual in queueing theory.
On the variance of the maximum of partial sums of n-exchangeable random variables with applications
Authors: Anis A. A. , Gharib M.
Published: April 2006

A general formula is obtained for the variance of the maximum of partial sums of n-exchangeable random variables, derived from a result of Spitzer's. The formula is applied in particular to obtain the variance of the maximum of adjusted rescaled partial sums of normal summands. This is of direct relevance to the Hurst effect.
On the envelope of a Gaussian random field
Authors: Adler R. J.
Published: April 2006

For homogeneous, two-dimensional random field ξ(t), t ∈ R2 we develop the ‘half' spectral theory sufficient to rigorously define its envelope η (t). We then specialise to the case of ξ Gaussian, which implies η is Rayleigh, and consider the mean value of a certain characteristic of the sets {t:η(t) ≧ u} (u ≧ 0). From this we deduce some qualitative information about the sample path behaviour of the Rayleigh field η .
On random divisions of a convex set
Authors: Janson Svante
Published: April 2006

This paper gives an elementary proof that, under some general assumptions, the number of parts a convex set in Rd is divided into by a set of independent identically distributed hyperplanes is asymptotically normally distributed. An example is given where the distribution of hyperplanes is ‘too singular' to satisfy the assumptions, and where a different limiting distribution appears.
The dependence of betting strategies on the probability of winning
Authors: Subelman Eduardo J.
Published: April 2006

We consider the optimal wagers to be made by a gambler facing cointossing games who desires to maximize the expected value of the utility of his final fortune in a fixed number n of plays. In the case of fixed probability of a win, the optimal bet is shown to be increasing in the probability. In the case of unknown probability of a win, the wager is shown to be monotone in the prior distribution under the monotone likelihood ratio ordering of these distributions.
Moment computations for subcritical branching processes
Authors: Lange Kenneth , Boehnke Michael , Carson Richard
Published: April 2006

The present paper considers methods for computing moments connected with subcritical multitype branching processes. By stressing the interplay between moment and cumulant structure, it is possible to prove simultaneously the existence of the moments. The kinds of moments considered are those arising in (1) times to extinction, (2) ultimate numbers of particles starting from a single particle, and (3) equilibrium numbers of particles for subcritical processes experiencing immigration.
First-order stochastic chemical reactions and oscillations in the variance
Authors: Hertzberg Richard C. , Gallucci Vincent F.
Published: April 2006

The general solution of a Markov model for first-order kinetics is developed as a sum of independent, multinomially distributed random processes. Fluctuations in the mean and variance functions are discussed and shown to be unrelated in time during the early phase of the reaction. Numerical examples are presented for two- and three-component systems.
Exponential spectra as a tool for the study of server-systems with several classes of customers
Authors: Keilson J.
Published: April 2006

For a single-server system having several Poisson streams of customers with exponentially distributed service times, busy period densities, waiting time densities, and idle state probabilities are completely monotone. The exponential spectra for such densities are of importance for understanding the transient behavior of such systems. Algorithms are given for the computation of such spectra. Applications to heavy traffic situations and priority systems are also discussed.
On the persistence of random genetic drift
Authors: Antonelli Peter L. , Morgan Kenneth
Published: April 2006

It is demonstrated that standard Brownian motion in the tangent plane at the centroid of frequency space does not well approximate the discrete Wright—Fisher process for more than 2N generations where N is the effective population size. This result is obtained using Wright's concept of negligible mutation rate for the study of systematic evolutionary effects together with Ludwig's notion of the persistence of a dynamical system. This work may be viewed as a mathematical elaboration of a portion of Wright's shifting balance theory of evolution.
On the first-order bilinear time series model
Authors: Pham Tuan Dinh , Tran Lanh Tat
Published: April 2006

The paper investigates some properties of the first-order bilinear time series model: stationarity and invertibility. Estimates of the parameters are obtained by a modified least squares method and shown to be strongly consistent.
Extreme values of independent stochastic processes
Authors: Brown Bruce M. , Resnick Sidney I.
Published: April 2006

The maxima of independent Weiner processes spatially normalized with time scales compressed is considered and it is shown that a weak limit process exists. This limit process is stationary, and its one-dimensional distributions are of standard extreme-value type. The method of proof involves showing convergence of related point processes to a limit Poisson point process. The method is extended to handle the maxima of independent Ornstein–Uhlenbeck processes.
Minimum contrast estimation in diffusion processes
Authors: Lánska Vĕra
Published: April 2006

This paper is concerned with the asymptotic theory of estimates of an unknown parameter in continuous-time Markov processes, which are described by non-linear stochastic differential equations. The maximum likelihood estimate and the minimum contrast estimate are investigated. For these estimates strong consistency and asymptotic normality are proved. The unknown parameter is assumed to take its values either in an open or in a compact set of real numbers.
An embedded level crossing technique for dams and queues
Authors: Brill P. H.
Published: April 2006

The new concept of embedded level crossings is combined with the old principle of stationary set balance to produce an alternative approach for obtaining the steady-state distribution of the level in a dam with general release rule. The method yields the steady state distribution of the customer waiting time in the GI/G/1 queue as a special case. Results for a dam in which the instantaneous release rate is proportional to the level, and for the M/G/1, GI/M/1, Ek/M/1 and D/M/1 queues are derived using the new technique.
A note on the limiting behaviour of discrete-time Markovian manpower models with inhomogeneous independent Poisson input
Authors: Mehlmann Alexander
Published: April 2006

Using the expectation recurrence equation of discrete-time Markovian manpower models, an asymptotic relation for the population numbers in various grades is derived.
Semi-Markov decision processes with polynomial reward
Authors: Rosberg Zvi
Published: April 2006

A semi-Markov decision process, with a denumerable multidimensional state space, is considered. At any given state only a finite number of actions can be taken to control the process. The immediate reward earned in one transition period is merely assumed to be bounded by a polynomial and a bound is imposed on a weighted moment of the next state reached in one transition. It is shown that under an ergodicity assumption there is a stationary optimal policy for the long-run average reward criterion. A queueing network scheduling problem, for which previous criteria are inapplicable, is given as an application.
A multitrap model for high-intensity reciprocity failure in the photographic grain
Authors: Anderson William J.
Published: April 2006

The response of the photographic grain to light is a non-deterministic process which is as yet not completely understood. This response, as measured by the photographic density, is usually taken to be a function of the product of incident light intensity and exposure time interval duration, but at extreme values of either of these two quantities, this is no longer true. This latter effect is called reciprocity-law failure.

This paper discusses a probabilistic model, similar to a multiserver queue, for high-intensity reciprocity failure.
The sojourn time in the GI/M/1 queue by processor sharing
Authors: Ramaswami V.
Published: April 2006

A queueing model of considerable interest in computer engineering is the processor-sharing model in which the server shares its fixed capacity equally among all units present in the system. Here, we derive the mean and the variance of the equilibrium sojourn time, and deduce that the variance of the sojourn time is larger for the processor-sharing model than for the corresponding FCFS model.
A threshold theorem for the Reed-Frost chain-binomial epidemic
Authors: Ball Frank
Published: April 2006

We prove a threshold theorem for the Reed–Frost chain-binomial model which is analogous to the threshold theorem of Williams (1971) for the general stochastic epidemic. We show that when the population size is large a ‘true epidemic’ occurs with a non-zero probability if and only if an initial infective individual infects on average more than one susceptible individual.
The existence of moments for stationary Markov chains
Authors: Tweedie R. L.
Published: April 2006

We give conditions under which the stationary distributionπof a Markov chain admits moments of the general form ∫f(x)π(dx), wherefis a general function; specific examples includef(x) =xrandf(x) =esx. In general the time-dependent moments of the chain then converge to the stationary moments. We show that in special cases this convergence of moments occurs at a geometric rate. The results are applied to random walk on [0, ∞).
Upper (lower) bounds on the mean of the maximum (minimum) of a number of random variables
Authors: Aven Terje
Published: April 2006

In this paper, we give some upper (lower) bounds on where the Xi's are real-valued random variables. Some applications are given.
On the asymptotic normality of the number of replications of a paired comparison
Authors: Menon V. V. , Indira N. K.
Published: April 2006

Consider the number Xm of comparisons made in a sequence of comparisons between two opponents, which terminates as soon as one opponent wins m comparisons. The convergence of Xm to the normal variable is completely characterized. The normal approximations to the probability function and to the distribution function of Xm are obtained for any sufficiently large m, together with estimates of the errors in these approximations. Similar results are obtained for the negative binomial distribution as well. Finally, some simple estimates of the mean, variance and the incomplete beta function with equal arguments are constructed.
Asymptotic distribution of the coefficient of cross-association based on a simple Markov-chain model
Authors: Vrbik Jan
Published: April 2006

The asymptotic distribution of the ‘coefficient of cross-association' between two sequences of nominal data is investigated, under the assumption that the sequences have been generated by means of a specific (n − 1)-parameter Markov-chain model, frequently used by geologists. A practical approximate formula for calculating the standard deviation of this distribution is presented, and the region of its applicability examined.
The residual process for non-linear regression
Authors: MacNeill Ian B. , Jandhyala V. K.
Published: April 2006

Limit processes for sequences of partial sums of non-linear regression residuals are obtained under assumptions on regressor functions imposed by Jennrich (1969). The limit process and covariance kernel are calculated explicitly for functions of exponential type.
The basic equations for a supplemented GSMP and its applications to queues
Authors: Miyazawa Masakiyo , Yamazaki Genji
Published: April 2006

A supplemented GSMP (generalized semi-Markov process) is a useful stochastic process for discussing fairly general queues including queueing networks. Although much work has been done on its insensitivity property, there are only a few papers on its general properties. This paper considers a supplemented GSMP in a general setting. Our main concern is with a system of Laplace–Stieltjes transforms of the steady state equations called the basic equations. The basic equations are derived directly under the stationary condition. It is shown that these basic equations with some other conditions characterize the stationary distribution. We mention how to get a solution to the basic equations when the solution is partially known or inferred. Their applications to queues are discussed.
A collision probability problem
Authors: Papaderou-Vogiatzaki Irini , Schneider Rolf
Published: April 2006

A random stream of convex particles in , all moving uniformly in the same direction, is given. A convex test body is brought into the stream by means of a random rigid motion, independent of the stream. The number of particles that hit the test body at a preassigned boundary set within unit time is a random variable. Its expected value is determined under different model assumptions.
Comment on ‘Corrected diffusion approximations in certain random walk problems'
Authors: Hogan Michael L.
Published: April 2006

Correction terms for the diffusion approximation to the maximum and ruin probabilities for a random walk with small negative drift, obtained by Siegmund (1979) in the exponential family case, are extended by different methods to some non-exponential family cases.
The substability and ergodicity of complicated queueing systems
Authors: Nakatsuka Toshinao
Published: April 2006

The substability and the ergodicity of various queueing models are discussed. This paper considers the vector-valued queueing process Xrn = (xrn,1,xrn,2, · ··) with non-negative components and a constant initial value Xrr= a. For this, the substability is derived under simple conditions by showing the finiteness of
With respect to the ergodicity, in order to make use of Borovkov's theorem, we additionally assume that the distribution of the interarrival of customers has non-bounded tail for any given past sequence.
Bell's inequality, probability modelling and quantum correlation experiments
Authors: Finch P. D.
Published: April 2006

Problems associated with setting up a probability model which generates the quantum theoretical probabilities for the two spin 1/2 particle system are examined. Arguments which claim to show that such a model cannot be constructed within classical probability theory under the assumption of local singlet states are also considered. It is shown that the model then in question is not a probability model in the sense that term is used elsewhere in science. An alternative model is proposed and its bearing on the Einstein-Bohr debate is briefly discussed.
A characterization of the gamma distribution from a random difference equation
Authors: Tollar Eric S.
Published: April 2006

A characterization of the gamma distribution is considered which arises from a random difference equation. A proof without characteristic functions is given that if V and Y are independent random variables, then the independence of V · Y and (1 – V) · Y results in a characterization of the gamma distribution (after excluding the trivial cases).
Stochastic motions on the 3-sphere governed by wave and heat equations
Authors: Orsingher Enzo
Published: April 2006

In this paper a random motion on the surface of the 3-sphere whose probability law is a solution of the telegraph equation in spherical coordinates is presented. The connection of equations governing the random motion with Maxwell equations is examined together with some qualitative features of its sample paths. Finally Brownian motion on the 3-sphere is derived as the limiting process of a random walk with latitude-changing probabilities.
A note on a randomized occupancy problem
Authors: Swensen Anders Rygh
Published: April 2006

Consider N urns into which n balls are dropped independently with equal probability of hitting each urn and constant probability p of staying in the urn. We find the characteristic function of the joint distribution of KN and LN where KN is the number of urns that have not been hit, and LN is the number of urns where all balls have fallen through. Furthermore, we study the asymptotic distribution of (KN, LN) as n, N → ∞ at various rates.
The high-order autocovariance structure of the telegraph wave
Authors: Renshaw Eric
Published: April 2006

Exact expressions are developed for the nth order autocovariance structure of the telegraph wave, the integral of which defines a biased correlated random walk.
M/G/1 queueing systems with returning customers
Authors: Greenberg Betsy S.
Published: April 2006

Single-channel queues with Poisson arrivals, general service distributions, and no queue capacity are studied. A customer who finds the server busy either leaves the system for ever or may return to try again after an exponentially distributed time. Steady-state probabilities are approximated and bounded in two different ways. We characterize the service distribution by its Laplace transform, and use this characterization to determine the better method of approximation.
Band-limited spectral estimation of autoregressive-moving-average processes
Authors: Thomson P. J.
Published: April 2006

Consider an autoregressive-moving-average process of given order where it is known that a number of moving-average roots are of unit modulus. Such a situation might arise, for example, when a time series has been differenced to induce stationarity by removing a non-stationary polynomial or seasonal trend. A band-limited spectral estimation procedure is proposed for estimating the coefficients of such a process and the asymptotic properties of the estimators investigated. The asymptotic theory is illustrated with reference to simulated and real data. A preliminary investigation of the use of Akaike's AIC criterion and this procedure to determine the number of roots of unit modulus (in the case where this is unknown) is also carried out by means of simulation.

The proposed band-limited spectral estimation procedure can also be used to take account of other possible effects met in practice. These include, for example, the band-limited response of a recording device or trend-contaminated low-frequency components.
Random cyclic transformations of points
Authors: Veitch J. G. , Watson G. S.
Published: April 2006

We consider the action of independent and identically distributed n × n circulants S1, S2, … on V = [v1, …, vn] whose columns are the positions of n points in ℝd. The positions of the n points after m transformations are the columns of W(m) = VS1 … Sm. We describe, in several ways, the shape of the configuration of the points W(m) as m →∞. When n = 3, 4 and d = 2, a special discussion in terms of Moebius transformations is given.
Notes on the stability of closed queueing networks
Authors: Sigman Karl
Published: April 2006

A new proof of the stability of closed Jackson-type queueing networks (with general service-time distributions) is given and sufficient conditions are given for obtaining Cesaro, weak and total variation convergence of the continuous-time joint queue length and residual service-time process to a limiting distribution. The result weakens the sufficient conditions (for stability) of Borovkov (1986) by allowing more general service-time distributions.
Autoregressive processes in optimization
Authors: Cipra Tomáš
Published: April 2006

Vector autoregressive processes of the first order are considered which are non-negative and optimize a linear objective function. These processes may be used in stochastic linear programming with a dynamic structure. By using Tweedie's results from the theory of Markov chains, conditions for geometric rates of convergence to stationarity (i.e. so-called geometric ergodicity) and for existence and geometric convergence of moments of these processes are obtained.
Regeneration in tandem queues with multiserver stations
Authors: Sigman Karl
Published: April 2006

A tandem queue with a FIFO multiserver system at each stage, i.i.d. service times and a renewal process of external arrivals is shown to be regenerative by modeling it as a Harris-ergodic Markov chain. In addition, some explicit regeneration points are found. This generalizes the results of Nummelin (1981) in which a single server system is at each stage and the result of Charlot et al. (1978) in which the FIFO GI/GI/c queue is modeled as a Harris chain. In preparing for our result, we study the random assignment queue and use it to give a new proof of Harris ergodicity of the FIFO queue.
On the properties of processes associated with a markov branching process
Authors: Gadag V. G. , Gupta R. P.
Published: April 2006

Consider a time-homogeneous Markov branching process. We construct reduced processes, based on whether the length of line of descent of particles of this process are (a) greater than or (b) at most equal to, τ units of time, for some fixed τ ≧ 0. We show that in both cases the reduced processes retain the branching property, but the latter does not retain the time homogeneity. We investigate finite-time and asymptotic properties of the reduced processes. Based on a realization of the original process and a realization of a reduced process, observed continuously over a time interval [0, T] for T > 0, we propose estimators for the different parameters involved, including qτ, the probability that the original process becomes extinct before τ units of time, and f(j)(qτ), the jth derivative of the offspring probability generating function f(s) at qτ when qτ is known. We study the properties of these estimators and derive their asymptotic distributions, under the assumption that the original process is supercritical.
Product-form queueing networks with negative and positive customers
Authors: Gelenbe Erol
Published: April 2006

We introduce a new class of queueing networks in which customers are either ‘negative' or ‘positive'. A negative customer arriving to a queue reduces the total customer count in that queue by 1 if the queue length is positive; it has no effect at all if the queue length is empty. Negative customers do not receive service. Customers leaving a queue for another one can either become negative or remain positive. Positive customers behave as ordinary queueing network customers and receive service. We show that this model with exponential service times, Poisson external arrivals, with the usual independence assumptions for service times, and Markovian customer movements between queues, has product form. It is quasi-reversible in the usual sense, but not in a broader sense which includes all destructions of customers in the set of departures. The existence and uniqueness of the solutions to the (nonlinear) customer flow equations, and hence of the product form solution, is discussed.
Sojourn times in single-server queues by negative customers
Authors: Harrison P. G. , Pitel E.
Published: April 2006

We derive expressions for the Laplace transform of the sojourn time density in a single-server queue with exponential service times and independent Poisson arrival streams of both ordinary, positive customers and negative customers which eliminate a positive customer if present. We compare first-come first-served and last-come first-served queueing disciplines for the positive customers, combined with elimination of the last customer in the queue or the customer in service by a negative customer. We also derive the corresponding result for processor-sharing discipline with random elimination. The results show differences not only in the Laplace transforms but also in the means of the distributions, in contrast to the case where there are no negative customers. The various combinations of queueing discipline and elimination strategy are ranked with respect to these mean values.
On ratios of random variables and generalised mortality rates
Authors: Roberts Leigh A.
Published: April 2006

We find the distribution function of a ratio of dependent random variables which can represent a generalised mortality rate in a demographic or life insurance context. Each death in the numerator and each unit of exposure in the denominator are weighted by a random sum at risk, which is assumed to follow a gamma distribution. General results on the existence of moments of ratios of random variables are established, and applied to show that the moments of the rates considered here depend in a simple way on the minimum number of entrants into the mortality investigation.
Factorial moments for random mappings by means of indicator variables
Authors: English Brian J.
Published: April 2006

A simple identity for the incomplete factorial of sums of zero-one variables is exploited to provide the factorial moments of the number of components and the number of cyclical elements of the random mapping (T, {pi}) considered by Ross (1981).
A distributed clustering process
Authors: Coffman E. G. , Courtois P.-J. , Gilbert E. N. , Piret Ph.
Published: April 2006

The points of a graph G will form clusters as a result of a flow process. Initially, points i of G own resources xi which are i.i.d. random real numbers. Afterwards, resources flow between points, but always from a point to a neighbor that has accumulated a larger total resource. Thus points with small resource tend to lose it and points with large resource tend to gain. Eventually the flow stops with only two kinds of points, nulls with no resource left and absorbers with such large resource that no neighbor can take it. The final resource at an absorber is a sum of certain initial resources xi, and the corresponding points i form one cluster. Analytical results are obtainable when G is the chain of integer points on the line. Probability distributions are derived for the distance between consecutive absorbers and the size of a cluster. Indeed these distributions do not involve the given distribution for the xi. The Laplace transform of the distribution of final resources at absorbers is derived but the distribution itself is obtained by a simulation. For general graphs G only partial results are obtained.
Evaluation of the decay parameter for some specialized birth-death processes
Authors: Kijima Masaaki
Published: April 2006

Let N(t) be an exponentially ergodic birth-death process on the state space {0, 1, 2, ···} governed by the parameters {λn, μn}, where µ0 = 0, such that λn = λ and μn = μ for all n ≧ N, N ≧ 1, with λ < μ. In this paper, we develop an algorithm to determine the decay parameter of such a specialized exponentially ergodic birth-death process, based on van Doorn's representation (1987) of eigenvalues of sign-symmetric tridiagonal matrices. The decay parameter is important since it is indicative of the speed of convergence to ergodicity. Some comparability results for the decay parameters are given, followed by the discussion for the decay parameter of a birth-death process governed by the parameters such that limn→∞λn = λ and limn→∞µn = μ. The algorithm is also shown to be a useful tool to determine the quasi-stationary distribution, i.e. the limiting distribution conditioned to stay in {1, 2, ···}, of such specialized birth-death processes.
A comparison theorem for conditioned Markov processes
Authors: Roberts G. O.
Published: April 2006

Intuitively, the effect of conditioning a one-dimensional process to remain below a certain (possibly time-dependent) boundary is to ‘push' the process downwards. This paper investigates the effect of such conditioning, and finds the class of processes for which our intuition is accurate. It is found that ordinary stochastic inequalities are in general unsuitable for making statements about such conditioned processes, and that a stronger type of inequality is more appropriate.

The investigation is motivated by applications in estimation of boundary hitting time distributions.
Equilibrium points for three games based on the Poisson process
Authors: Dixon M. T.
Published: April 2006

An arbitrary number of competitors are presented with independent Poisson streams of offers consisting of independent and identically distributed random variables having the uniform distribution on [0, 1]. The players each wish to accept a single offer before a known time limit is reached and each aim to maximize the expected value of their offer. Rejected offers may not be recalled, but they are passed on to the other players according to a known transition matrix. This paper finds equilibrium points for two such games, and demonstrates a two-player game with an equilibrium point under which the player with the faster stream of offers has a lower expected reward than his opponent.
Nested variational inequalities and related optimal starting–stopping problems
Authors: Sun M.
Published: April 2006

This paper introduces several versions of starting-stopping problem for the diffusion model defined in terms of a stochastic differential equation. The problem could be regarded as a stochastic differential game in which the player can only decide when to start the game and when to quit the game in order to maximize his fortune. Nested variational inequalities arise in studying such a problem, with which we are able to characterize the value function and to obtain optimal strategies.
A remark on the proof of Itô's formula for C2 functions of continuous semimartingales
Authors: Kendall Wilfrid S.
Published: April 2006

The Itô formula is the fundamental theorem of stochastic calculus. This short note presents a new proof of Itô's formula for the case of continuous semimartingales. The new proof is more geometric than previous approaches, and has the particular advantage of generalizing immediately to the multivariate case without extra notational complexity.
Random polymorphisms and random evolutionarily stable strategies: a comparison
Authors: Haigh John
Published: April 2006

Recently, the properties of ESSs for random payoff matrices, and stable polymorphisms for random fitness matrices, have been investigated. These problems are very closely related, and some similarities and differences are examined here. In contrast to some earlier work,non-robustness of the conclusions, to changes in the distribution of the random matrices, are found in two areas: in the asymptotic number of polymorphisms (or ESSs) whose support is a given size, and in the location of a polymorphism (or ESS) whose size of support is 2 or 3, in a large matrix.
A bivariate counting process
Authors: Watson Ray , Yip Paul
Published: April 2006

We consider a bivariate Markov counting process with transition probabilities having a particular structure, which includes a number of useful population processes. Using a suitable random time-scale transformation, we derive some probability statements about the process and some asymptotic results. These asymptotic results are also derived using martingale methods. Further, it is shown that these methods and results can be used for inference on the rate parameters for the process. The general epidemic model and the square law conflict model are used as illustrative examples.