bluuebunny/crossref_metadata_2025 huggingface dataset:
School Psychologists' Job Satisfaction
Authors: Worrell Travis G. , Skaggs Gary E. , Brown Michael B.
Published: April 2006

School psychologists have consistently been found to have high levels of job satisfaction. The purpose of this study was to identify the current level of job satisfaction for practicing school psychologists and examine the changes over the past 22 years. Surveys were sent to 500 randomly selected members of the National Association of School Psychologists, and the results were compared to previous national surveys conducted in 1992 and 1982. Job satisfaction has slightly increased over the previous 22 years. School psychologists continue to be most satisfied with the social service, independence and values aspects of their jobs. They are also very satisfied with their co-workers and job activities. Satisfaction with job security, compensation and working conditions improved the most over the 20-year time span. Opportunities for advancement and school system policies and practices remain sources of job dissatisfaction. Aspiring school psychologists can take some measure of assurance that school psychology offers a career in which one can do work that provides an important service to others and is consistent with one's values.
Peer Mediation
Authors: Shamir Adina , Tzuriel David , Rozen Merav
Published: April 2006

The objectives of the current study were to examine: (a) the effects of the Peer Mediation with Young Children (PMYC) program on mediators’ and learners’ mediation style in the context of maths teaching; and (b) the interaction effects of the intervention program, children's verbal ability, and maths level on pre- to postintervention improvement in maths and mediation style. The sample was composed of 108 pupils (54 mediator—learner dyads), equally divided between an experimental and a control group. In each dyad, the mediator was from Grade 3 and the learner from Grade 2. Mediators and learners in each pair were matched in a counterbalanced design (2 × 2) according to their level of maths skills (high versus low). The experimental children received the PMYC program whereas the control children received general preparation for peer-assisted learning only. Following the PMYC intervention, all children participated in a peer-mediation condition where the mediators taught their younger peers how to solve maths problems. The interaction was videotaped for 25 minutes and analysed by the Observation of Mediation Instrument. The main findings showed that the experimental children obtained significantly higher scores on all mediation criteria and improved their pre- to post-intervention scores in maths to a greater degree than did the control children. These findings are explained in relation to Vygotsky's and Feuerstein's theories in addition to previous findings on peer mediation.
ICT Training: INASP workshops for African university library staff
Authors: Belcher Martin , Gwynn Sara , Rosenberg Diana
Published: April 2006

In 1999, INASP began an ICT-related training programme for African university librarians using a ‘travelling’ methodology. This methodology and the development of the programme over the next six years and into the future are described and evaluated. African librarians are generally happy with this training approach. But whether it has assisted academic staff and student to better exploit the potential of the Internet has yet to be proved.
Special Section: The Adolescent Experience: From Omnipotence to Delinquency
Authors: Millar David
Published: April 2006

This paper attempts to look at the adolescent experience as a kind of tertiary stage of omnipotent development. If this ‘third time lucky’ scenario is played out against a benign or benevolent background then more ordinary development ensues. If met with belligerence, fear or retaliation then a route to delinquency may be opened up. An adolescent therapy group is used to illustrate this thesis.
Special Section: Psychoanalytic and Group-Analytic Perspectives in Forensic Psychotherapy
Authors: Hoffmann Klaus , Kluttig Tilman
Published: April 2006

The emphasis on empirically-founded forensic treatments puts psychoanalytic approaches in a defensive position. This article shows how essential individual and group-analytic findings are in psychotherapy with mentally ill offenders. These findings are often used by behavioural therapists to present their programs in realistic situations. The experiences of the psychotherapy ward in Reichenau Mental Hospital exemplify these findings.
Spirits of ‘Dark Finance’ in Thailand
Authors: Klima Alan
Published: April 2006

Moral discourses condemning Asian finance since the 1997 Thai currency crash have trickled down to small-time financial practices within informal money markets of Thailand. These practices include personal moneylending, gambling, underground lotteries, and number forecasting by spirit mediums. Moral devaluation of these socially complex practices, even inadvertently by anthropologists who might classify them as ‘occult’ or as ‘casino capitalism’, may obscure forms of economy that can question the authority of knowledge that backs international financial liberalization.
Newspapers' transition from women's to style pages
Authors: Harp Dustin
Published: April 2006

After nearly a century of publishing explicitly named women's pages, US newspapers starting in 1969 and into the 1970s began renaming them ‘style’ or ‘lifestyle’ sections, theoretically meaning they were for a general audience. This research investigates industry discourse during this time to determine what those in newsrooms were thinking about this transition. Seventy-two articles from three newspaper trade publications from 1969 through 1975 reveal that editors and reporters were most concerned with including serious content in these sections and unconcerned with the names of the sections. In fact the women editors of these style pages, who dominated the discourse, indicated that even after renaming the sections industry insiders thought of them as for and about women. The analysis also revealed that newsroom constraints, particularly those placed on lower level staff by male editors, prevented women editors of these women's/style sections from constructing the pages they desired.
Community Coalitions to Control Chronic Disease: Allies Against Asthma as a Model and Case Study
Authors: Clark Noreen M. , Doctor Linda Jo , Friedman Amy R. , Lachance Laurie L. , Houle Christy R. , Geng Xin , Grisso Jeane Ann
Published: April 2006

There is a rich and extensive literature regarding coalitions as vehicles for amassing resources, influence, and energy in pursuit of a health goal. Despite insufficient empirical data regarding outcome, a number of observers have posited the aspects of coalition processes thought to lead to goal attainment. The supplement, which this article is part of, is devoted to an examination of how these elements fitted together (or did not) in the seven areas across the United States where Allies coalitions devoted themselves to achieving asthma control. The aim of this article is to present the theoretical bases for the work of the coalitions. It illustrates and emphasizes how the community context influenced coalition development, how membership was involved in and assessed coalition processes and structures, and the community-wide actions that were instituted and the capacities they were trying to strengthen.
From Formation to Action: How Allies Against Asthma Coalitions Are Getting the Job Done
Authors: Butterfoss Frances D. , Gilmore Lisa A. , Krieger James W. , Lachance Laurie L. , Lara Marielena , Meurer John R. , Orians Carlyn E. , Peterson Jane W. , Rose Shyanika W. , Rosenthal Michael P.
Published: April 2006

Coalitions develop in and recycle through stages. At each stage (formation, implementation, maintenance, and institutionalization), certain factors enhance coalition function, accomplishment of tasks, and progression to the next stage. The Allies Against Asthma coalitions assessed stages of development through annual member surveys, key informant interviews of 16 leaders from each site, and other evaluation tools. Results indicate all coalitions completed formation and implementation, six achieved maintenance, and five are in the institutionalization stage. Differences among coalitions can be attributed to their maturity and experience working within a coalition framework. Participants agreed that community mobilization around asthma would not have happened without coalitions. They attributed success to being responsive to community needs and developing comprehensive strategies, and they believed that partners’ goals were more innovative and achievable than any institution could have created alone.
Methylation regulates the intracellular protein-protein and protein-RNA interactions of FMRP
Authors: Dolzhanskaya Natalia , Merz George , Aletta John M. , Denman Robert B.
Published: April 2006

FMRP, the fragile X mental retardation protein, is an RNA-binding protein that interacts with ∼4% of fetal brain mRNA. We have recently shown that a methyltransferase (MT) co-translationally methylates FMRP in vitro and that methylation modulates the ability of FMRP to bind mRNA. Here, we recapitulate these in vitro data in vivo, demonstrating that methylation of FMRP affects its ability to bind to FXR1P and regulate the translation of FMRP target mRNAs. Additionally, using double-label fluorescence confocal microscopy, we identified a subpopulation of FMRP-containing small cytoplasmic granules that are distinguishable from larger stress granules. Using the oxidative-stress induced accumulation of abortive pre-initiation complexes as a measure of the association of FMRP with translational components, we have demonstrated that FMRP associates with ribosomes during initiation and, more importantly, that methylation regulates this process by influencing the ratio of FMRP-homodimer-containing mRNPs to FMRP-FXR1P-heterodimer-containing mRNPs. These data suggest a vital role for methylation in normal FMRP functioning.
Slick grit: auteurship versus mimicry in three films by Francisco Lombardi
Authors: Hart Stephen
Published: April 2006

This article argues that contemporary Latin American cinema offers a new slant on the traditional notion of auteurship since it combines a gritty view of life with a slick cinematographic vision, and the work of the Peruvian film director, Francisco Lombardi (b. 1949) is used as a test
case to probe this hypothesis. Lombardi's work offers a particularly interesting field within which to investigate the applicability of the notion of auteurship because a number of his films are based on literary classics, namely La ciudad y los perros (1985), Pantalen y las visitadoras
(1999), both based on novels by Mario Vargas Llosa, and No se lo digas a nadie (1998), which is inspired by Jaime Bayly's novel of the same title. The article sets out, by a process of filmic subtraction, to measure the originality of Lombardi's vision as compared to the world-view
expressed within each of the novels.
Leaving an interval in limited playing time
Authors: Heath David , Kertz Robert P.
Published: April 2006

A player starts at x in (-G, G) and attempts to leave the interval in a limited playing time. In the discrete-time problem, G is a positive integer and the position is described by a random walk starting at integer x, with mean increments zero, and variance increment chosen by the player from [0, 1] at each integer playing time. In the continuous-time problem, the player's position is described by an Ito diffusion process with infinitesimal mean parameter zero and infinitesimal diffusion parameter chosen by the player from [0, 1] at each time instant of play. To maximize the probability of leaving the interval (–G, G) in a limited playing time, the player should play boldly by always choosing largest possible variance increment in the discrete-time setting and largest possible diffusion parameter in the continuous-time setting, until the player leaves the interval. In the discrete-time setting, this result affirms a conjecture of Spencer. In the continuous-time setting, the value function of play is identified.
The growth and composition of branching populations
Authors: Jagers Peter , Nerman Olle
Published: April 2006

A single-type general branching population develops by individuals reproducing according to i.i.d. point processes on R+, interpreted as the individuals' ages. Such a population can be measured or counted in many different ways: those born, those alive or in some sub-phase of life, for example. Special choices of reproduction point process and counting yield the classical Galton–Watson or Bellman–Harris process. This reasonably self-contained survey paper discusses the exponential growth of such populations, in the supercritical case, and the asymptotic stability of composition according to very general ways of counting. The outcome is a strict definition of a stable population in exponential growth, as a probability space, a margin of which is the well-known stable age distribution.
Stationary queue-length and waiting-time distributions in single-server feedback queues
Authors: Disney Ralph L. , König Dieter , schmidt Volker
Published: April 2006

For M/GI/1/∞ queues with instantaneous Bernoulli feedback time- and customer-stationary characteristics of the number of customers in the system and of the waiting time are investigated. Customer-stationary characteristics are thereby obtained describing the behaviour of the queueing processes, for example, at arrival epochs, at feedback epochs, and at times at which an arbitrary (arriving or fed-back) customer enters the waiting room. The method used to obtain these characteristics consists of simple relationships between them and the time-stationary distribution of the number of customers in the system at an arbitrary point in time. The latter is obtained from the wellknown Pollaczek–Khinchine formula for M/GI/1/∞ queues without feedback.
Improved bounds for the variance of the busy period of the M/G/∞ queue
Authors: Sathe Y. S.
Published: April 2006

Bounds obtained by Ramalhoto [1] for the variance of the busy period of an M/G/∞ queue are improved.
Records in the presence of a linear trend
Authors: Ballerini Rocco , Resnick Sidney I.
Published: April 2006

Records from the sequenceYn=Xn+cn, n≧ 1 are analyzed, where {Xn} is a strictly stationary random sequence. We prove various limit theorems for the record rate, record times, and record values. The situation when {Xn} is a stationary Gaussian process is considered with special attention given to Gaussian ARMA sequences. Data for the 400 and 800 metre races are used to illustrate these results.
Optimal stopping and dynamic allocation
Authors: Chang Fu , Lai Tze Leung
Published: April 2006

A class of optimal stopping problems for the Wiener process is studied herein, and asymptotic expansions for the optimal stopping boundaries are derived. These results lead to a simple index-type class of asymptotically optimal solutions to the classical discounted multi-armed bandit problem: given a discount factor0<β <1andkpopulations with densities from an exponential family, how shouldx1,x2,… besampled sequentially from these populations to maximize the expected value of Ʃ∞1βi−1xi, in ignorance of the parameters of the densities?
A transient solution to anM/M/1 queue: a simple approach
Authors: Parthasarathy P. R.
Published: April 2006

A time-dependent solution for the number in a single-server queueing system with Poisson arrivals and exponential service times is derived in a direct way.
Filtering of Markov renewal queues, IV: Flow processes in feedback queues
Authors: Hunter Jeffrey J.
Published: April 2006

This paper is a continuation of the study of a class of queueing systems where the queue-length process embedded at basic transition points, which consist of ‘arrivals’, ‘departures’ and ‘feedbacks’, is a Markov renewal process (MRP). The filtering procedure of Çinlar (1969) was used in [12] to show that the queue length process embedded separately at ‘arrivals’, ‘departures’, ‘feedbacks’, ‘inputs’ (arrivals and feedbacks), ‘outputs’ (departures and feedbacks) and ‘external’ transitions (arrivals and departures) are also MRP. In this paper expressions for the elements of each Markov renewal kernel are derived, and thence expressions for the distribution of the times between transitions, under stationary conditions, are found for each of the above flow processes. In particular, it is shown that the inter-event distributions for the arrival process and the departure process are the same, with an equivalent result holding for inputs and outputs. Further, expressions for the stationary joint distributions of successive intervals between events in each flow process are derived and interconnections, using the concept of reversed Markov renewal processes, are explored. Conditions under which any of the flow processes are renewal processes or, more particularly, Poisson processes are also investigated. Special cases including, in particular, the M/M/1/N and M/M/1 model with instantaneous Bernoulli feedback, are examined.
Heavy traffic limit theorems for a queueing system in which customers join the shortest line
Authors: Hanqin Zhang , Rongxin Wang
Published: April 2006

The queueing system considered in this paper consists of r independent arrival channels and s independent service channels, where, as usual, the arrival and service channels are independent. In the queueing system, each server of the system has his own queue and arriving customers join the shortest line in the system. We give functional central limit theorems for the stochastic processes characterizing this system after appropriately scaling and translating the processes in traffic intensity ρ > 1.
On the asymptotic behaviour of the extinction time of the simple branching process
Authors: Pakes Anthony G.
Published: April 2006

The time to extinction of a subcritical Galton–Watson branching process and the time of last mutation of its infinite-alleles version are maxima of independent random variables having an upper tail of geometric type, and hence they are not attracted to any extreme value distribution. It is shown that Anderson's asymptotic results for maxima of discrete variates are applicable, and this rectifies a false assertion made in respect to the infinite-alleles simple branching process.
On some diffusion approximations to queueing systems
Authors: Giorno V. , Nobile A. G. , Ricciardi L. M.
Published: April 2006

For a class of models of adaptive queueing systems an exact diffusion approximation is derived with the aim of obtaining information on the evolution of the systems. Our approximating diffusion process includes the Wiener and the Ornstein–Uhlenbeck processes with reflecting boundaries at 0. The goodness of the approximations is thoroughly discussed and the closed-form solutions obtained for the diffusion processes are compared with those holding for the queueing system in order to investigate the conditions under which reliable information can be obtained from the approximating continuous models. For the latter the transient behaviour is quantitatively analysed and the distribution of the busy period is determined in closed form.
Routing in circuit-switched networks: optimization, shadow prices and decentralization
Authors: Kelly F. P.
Published: April 2006

How should calls be routed or capacity allocated in a circuit-switched communication network so as to optimize the performance of the network? This paper considers the question, using a simplified analytical model of a circuit-switched network. We show that there exist implicit shadow prices associated with each route and with each link of the network, and that the equations defining these prices have a local or decentralized character. We illustrate how these results can be used as the basis for a decentralized adaptive routing scheme, responsive to changes in the demands placed on the network.
On the limit behavior of a multicompartment storage model with an underlying Markov chain
Authors: Tollar Eric S.
Published: April 2006

The present paper considers a multicompartment storage model with one-way flow. The inputs and outputs for each compartment are controlled by a denumerable-state Markov chain. Assuming finite first and second moments, it is shown that the amounts of material in certain compartments converge in distribution while for others they diverge, based on appropriate first-moment conditions on the inputs and outputs. It is also shown that the diverging compartments under suitable normalization converge to functionals of Brownian motion, independent of those compartments which converge without normalization.
Locally asymptotic normality of Gibbs models on a lattice
Authors: Mase Shigeru
Published: April 2006

We consider the statistical estimation problem of potential functions of Gibbs models on the plane lattice. We assume that the area on which a random point pattern is observed is sufficiently large and take an asymptotic point of view. The main result is to show the locally asymptotic normality of the Gibbs model under certain conditions. From this result we can show the optimality of the maximum likelihood estimator employing known results about locally asymptotic normal families, though a practical computation of the maximum likelihood estimator presents difficulties. An estimation procedure based on the method of moments is also proposed.
Comparison of optimal value and constrained maxima expectations for independent random variables
Authors: Kertz Robert P.
Published: April 2006

For all uniformly bounded sequences of independent random variables X1, X2, ···, a complete comparison is made between the optimal value V(X1, X2, ···) = sup {EXt:t is an (a.e.) finite stop rule for X1,X2, ···} and , where Mi(X1,X2, ···) is the ith largest order statistic for X1, X2, ··· In particular, for k> 1, the set of ordered pairs {(x, y):x = V(X1, X2, ···) and for some independent random variables X1, X2, ··· taking values in [0, 1]} is precisely the set , where Bk(0) = 0, Bk(1) = 1, and for The result yields sharp, universal inequalities for independent random variables comparing two choice mechanisms, the mortal&s value of the game V(X1, X2, ···) and the prophet&s constrained maxima expectation of the game . Techniques of proof include probability- and convexity-based reductions; calculus-based, multivariate, extremal problem analysis; and limit theorems of Poisson-approximation type. Precise results are also given for finite sequences of independent random variables.
A derivation of the information criteria for selecting autoregressive models
Authors: Bhansali R. J.
Published: April 2006

The Akaike information criterion, AIC, for autoregressive model selection is derived by adopting −2Ttimes the expected predictive density of a future observation of an independent process as a loss function, whereTis the length of the observed time series. The conditions under which AIC provides an asymptotically unbiased estimator of the corresponding risk function are derived. When the unbiasedness property fails, the use of AIC is justified heuristically. However, a method for estimating the risk function, which is applicable for all fitted orders, is given. A derivation of the generalized information criterion, AICα, is also given; the loss function used being obtained by a modification of the Kullback-Leibler information measure. Results paralleling those for AIC are also obtained for the AICαcriterion.
On the asymptotic distributions of maxima of trigonometric polynomials with random coefficients
Authors: Turkman K. F. , Walker A. M.
Published: April 2006

Let {εt,t =1, 2, ···,n} be a sequence of mutually independent standard normal random variables. LetXn(λ) andYn(λ) be respectively the real and imaginary parts ofexpiλt, and let. It is shown that asntends to∞, the distribution functions of the normalized maxima of the processes {Xn(λ)}, (Yn(λ)}, {In(λ)} over the interval λ∈ [0,π] each converge to the extremal distribution function exp [–e–x], —∞ <x<∞.

It is also shown that these results can be extended to the case where {εt} is a stationary Gaussian sequence with a moving-average representation.
Optimal group preventive maintenance of a system with observable state parameter
Authors: Gertsbakh I. B.
Published: April 2006

A group of n independent identical machines with exponential lifetimes is considered. Repair is made simultaneously for all failed machines. It is possible to observe the ‘state parameter', i.e. the number of operating machines. It is proved that for two types of critieria (minimal cost per time unit and maximal return per time unit) the optimal repair policy is of the following type: repair when the number of failed machines reaches some prescribed number .
A note on stochastic bounds for queueing networks
Authors: Tsoucas Pantelis , Walrand Jean
Published: April 2006

Recently, Massey [1] proved that the vector of queue lengths of some queueing networks is stochastically dominated at any given time by that of a corresponding system of parallel M/M/l queues. This result is interesting, even though the bounds are generally quite conservative, in that the transient behavior of independent parallel M/M/l queues is considerably easier to analyze than that of a network.

This note provides an alternative proof of a generalized form of that result.
Analysis of a non-preemptive priority multiserver queue
Authors: Gail H. R. , Hantler S. L. , Taylor B. A.
Published: April 2006

We consider a non-preemptive priority head of the line queueing system with multiple servers and two classes of customers. The arrival process for each class is Poisson, and the service times are exponentially distributed with different means. A Markovian state description consists of the number of customers of each class in service and in the queue. We solve a matrix equation to obtain the generating function of the equilibrium probability distribution by analyzing singularities of the equation coefficients, which are meromorphic matrices of two complex variables. We then obtain the mean waiting times for each class.
Ruin probabilities expressed in terms of storage processes
Authors: Asmussen Søren , Petersen Søren Schock
Published: April 2006

It is shown by a simple sample path argument that the ruin probabilities for a risk reserve process with premium ratep(r) depending on the reserverand finite or infinite horizon are related in a simple way to the state probabilities of a compound Poisson dam with the same release ratep(r) at contentr.In the infinite horizon case, this result has been established by Harrison and Resnick (1978), and in the finite horizon case with constantpit extends well-known relations to theM/G/1 virtual waiting time.
One-dimensional classical scattering processes and the diffusion limit
Authors: Kendall Wilfrid S. , Westcott Mark
Published: April 2006

The method of Skorokhod embedding, that is to say of coupling to Brownian motion, is used to establish the asymptotic behaviour of one-dimensional scattering processes.
Multivariate hazard rates and stochastic ordering
Authors: Shaked Moshe , Shanthikumar J. George
Published: April 2006

Properties of the conditional hazard rates ofX1, · ··,XnandY1, · ··,Yn,which imply (X1, · ··,Xn)(Y1, · ··,Yn), are found. These are used to find conditions on the hazard rates of T = (T1, · ··,Tn) which ensure thatThas the MIHR |property of Arjas (1981a) and the ‘weakened by failure’ property of Arjas and Norros (1984). Applications for load-sharing model and multivariate imperfect repair are given.
Optimal capacity expansion under uncertainty
Authors: Davis M. H. A. , Dempster M. A. H. , Sethi S. P. , Vermes D.
Published: April 2006

Capacity expansion is the process of providing new facilities over time to meet rising demand. A general mathematical model of this process is presented, incorporating uncertain future demand (including the possibility of ‘surprises’), non-zero lead times and random cost overruns. In this model the decision maker controls the rate of investment in the current expansion project. Optimization is studied by methods of stochastic control theory. Numerical algorithms are presented which determine the optimal policy in some simple cases.
Second-order approximation to the characteristic function of certain point-process integrals
Authors: Ellis Steven P.
Published: April 2006

A general way to look at kernel estimates of densities is to regard them as stochastic integrals with respect to a spatial point process. Under regularity conditions these behave asymptotically as if the point process were Poisson. However, this Poisson approximation may not work well if the data exhibits a lot of clustering. In this paper a more refined approximation to the characteristic functions of the integrals is developed. For clustered data, a ‘Gauss–Poisson’ approximation works better than the Poisson.
On Niu&s conjecture for tandem queues
Authors: Greenberg Betsy S.
Published: April 2006

We show that Niu&s (1980) conjecture is true for Poisson arrivals and light traffic. We also show that a weak version of the conjecture is true for a special case in heavy traffic.
Fluctuations near homogeneous states of chemical reactions with diffusion
Authors: Kotelenez Peter
Published: April 2006

Conditions are given under which a space-time jump Markov process describing the stochastic model of non-linear chemical reactions with diffusion converges to the homogeneous state solution of the corresponding reaction-diffusion equation. The deviation is measured by a central limit theorem. This limit is a distribution-valued Ornstein–Uhlenbeck process and can be represented as the mild solution of a certain stochastic partial differential equation.
Stability of Markovian processes I: criteria for discrete-time Chains
Authors: Meyn Sean P. , Tweedie R. L.
Published: April 2006

In this paper we connect various topological and probabilistic forms of stability for discrete-time Markov chains. These include tightness on the one hand and Harris recurrence and ergodicity on the other. We show that these concepts of stability are largely equivalent for a major class of chains (chains with continuous components), or if the state space has a sufficiently rich class of appropriate sets (‘petite sets').

We use a discrete formulation of Dynkin's formula to establish unified criteria for these stability concepts, through bounding of moments of first entrance times to petite sets. This gives a generalization of Lyapunov–Foster criteria for the various stability conditions to hold. Under these criteria, ergodic theorems are shown to be valid even in the non-irreducible case. These results allow a more general test function approach for determining rates of convergence of the underlying distributions of a Markov chain, and provide strong mixing results and new versions of the central limit theorem and the law of the iterated logarithm.
Further monotonicity properties of renewal processes
Authors: Kijima Masaaki
Published: April 2006

In a discrete-time renewal process {Nk, k = 0, 1, ·· ·}, let Zk and Ak be the forward recurrence time and the renewal age, respectively, at time k. In this paper, we prove that if the inter-renewal time distribution is discrete DFR (decreasing failure rate) then both {Ak, k = 0, 1, ·· ·} and {Zk, k = 0, 1, ·· ·} are monotonically non-decreasing in k in hazard rate ordering. Since the results can be transferred to the continuous-time case, and since the hazard rate ordering is stronger than the ordinary stochastic ordering, our results strengthen the corresponding results of Brown (1980). A sufficient condition for {Nk+m – Nk, k = 0, 1, ·· ·} to be non-increasing in k in hazard rate ordering as well as some sufficient conditions for the opposite monotonicity results are given. Finally, Brown's conjecture that DFR is necessary for concavity of the renewal function in the continuous-time case is discussed.
On a relationship between processor-sharing queues and Crump–Mode–Jagers branching processes
Authors: Grishechkin Sergei
Published: April 2006

TheM/G/1 queue with batch arrivals and a queueing discipline which is a generalization of processor sharing is studied by means of Crump–Mode–Jagers branching processes. A number of theorems are proved, including investigation of heavy traffic and overloaded queues. Most of the results obtained are also new for theM/G/1 queue with processor sharing. By use of a limiting procedure we also derive new results concerningM/G/1 queues with shortest residual processing time discipline.
Superposition of renewal processes
Authors: Teresalam C. Y. , Lehoczky John P.
Published: April 2006

This paper extends the asymptotic results for ordinary renewal processes to the superposition of independent renewal processes. In particular, the ordinary renewal functions, renewal equations, and the key renewal theorem are extended to the superposition of independent renewal processes. We fix the number of renewal processes,p,and study the asymptotic behavior of the superposition process when time,t,is large. The key superposition renewal theorem is applied to the study ofqueueing systems.
On some examples of quadratic functionals of Brownian motion
Authors: Donati-Martin C. , Yor M.
Published: April 2006

During the last few years, several variants of P. Lévy's formula for the stochastic area of complex Brownian motion have been obtained. These are of interest in various domains of applied probability, particularly in relation to polymer studies. The method used by most authors is the diagonalization procedure of Paul Lévy.

Here we derive one such variant of Lévy's formula, due to Chan, Dean, Jansons and Rogers, via a change of probability method, which reduces the computation of Laplace transforms of Brownian quadratic functionals to the computations of the means and variances of some adequate Gaussian variables.

We then show that with the help of linear algebra and invariance properties of the distribution of Brownian motion, we are able to derive simply three other variants of Lévy's formula.
On a family of prior distributions for a class of Bayesian search models
Authors: Glazebrook K. D.
Published: April 2006

We propose a two-parameter family of conjugate prior distributions for the number of undiscovered objects in a class of Bayesian search models. The family contains the one-parameter Euler and Heine families as special cases. The two parameters may be interpreted respectively as an overall success rate and a rate of depletion of the source of objects. The new family gives enhanced flexibility in modelling.
On continuous image models and image analysis in the presence of correlated noise
Authors: Hall Peter , Koch Inge
Published: April 2006

Most theoretical studies of image processing employ discrete image models. While that might be a good approximation to digital analysis, it severely restricts the class of tractable models for the blur component of image degradation, and concentrates excessive attention on specialized features of the pixel lattice. It is analogous to modelling all real statistical data using discrete distributions, which is clearly unnecessary. In this paper we study a continuous model for image analysis, in the presence of systematic degradation via a point spread function and stochastic degradation by a second-order stationary random field. Thus, we depart from the restrictive white-noise models which are commonly used in the theory of image analysis. We establish a general result which describes the performance of optimal image processing methods when the noise process has short-range dependence. Concise limits to resolution are derived, depending on image type, point spread function and noise correlation. These results are developed in important special cases, giving explicit formulae for optimal smoothing sets and convergence rates.
On variation in birth processes
Authors: Faddy M. J.
Published: April 2006

Birth processes with piecewise linear birth rates are analysed, and numerical results suggest that, relative to the linear case, convex birth rates increase variability and concave birth rates decrease variability.
The neutral two-locus model as a measure-valued diffusion
Authors: Ethier S. N. , Griffiths R. C.
Published: April 2006

The neutral two-locus model in population genetics is reformulated as a measure-valued diffusion process and is shown under certain conditions to have a unique stationary distribution and be weakly ergodic. The limits of the process and its stationary distribution as the recombination parameter tends to infinity are found. Genealogies are incorporated into the model, and it is shown that a random sample of sizenfrom the population at stationarity has a common ancestor.
The collector's problem with group drawings
Authors: Stadje Wolfgang
Published: April 2006

We consider sampling with replacement of equiprobable groups of a fixed sizemfrom a finite populationS.Given a subsetA⊂S, the distributions of (a) the number of distinct elements ofAin a sample of sizekand (b) the sample size necessary to obtain at least saynelements ofAare given. Neat formulas are given especially for the expected values of these, as well as of some related random variables. Further we derive an optimal strategy to collect all elements ofSunder the assumptions that sampling one group costsαmonetary units and that it is possible to purchase the elements which are missing at the end of the sampling procedure at a price ofβ>α/mper element.
Stochastic Discounting, Aggregate Claims, and the Bootstrap
Authors: Aebi M. , Embrechts P. , Mikosch T.
Published: April 2006

Obtaining good estimates for the distribution function of random variables like(‘perpetuity’) and(‘aggregate claim amount’), where the (Yi), (Zi) are independent i.i.d. sequences and (N(t)) is a general point process, is a key question in insurance mathematics. In this paper, we show how suitably chosen metrics provide a theoretical justification for bootstrap estimation in these cases. In the perpetuity case, we also give a detailed discussion of how the method works in practice.
Conditioned Limit Theorems for the Difference of Waiting Time and Queue Length
Authors: Szczotka Władysław , Topolski Krzysztof
Published: April 2006

Consider the GI/G/1 queueing system with traffic intensity 1 and let wk and lk denote the actual waiting time of the kth unit and the number of units present in the system at the kth arrival including the kth unit, respectively. Furthermore let τ denote the number of units served during the first busy period and μ the intensity of the service. It is shown that as k →∞, where a is some known constant, , , and are independent, is a Brownian meander and is a Wiener process. A similar result is also given for the difference of virtual waiting time and queue length processes. These results are also extended to a wider class of queueing systems than GI/G/1 queues and a scheme of series of queues.
The infinitely-many-neutral-alleles diffusion model by ages
Authors: Ethier S. N.
Published: April 2006

We discuss two formulations of the infinitely-many-neutral-alleles diffusion model that can be used to study the ages of alleles. The first one, which was introduced elsewhere, assumes values in the set of probability distributions on the set of alleles, and the ages of the alleles can be inferred from its sample paths. We illustrate this approach by proving a result of Watterson and Guess regarding the probability that the most frequent allele is oldest. The second diffusion model, which is new, assumes values in the set of probability distributions on the set of pairs (x, a), where x is an allele and a is its age. We illustrate this second approach by proving an extension of the Ewens sampling formula to age-ordered samples due to Donnelly and Tavaré.
Asymptotic tail behaviour of Poisson mixtures by applications
Authors: Willmot Gordon E.
Published: April 2006

This expository paper deals with the right tail behaviour of a class of Poisson mixtures. An Abelian-type result is obtained using basic theory of regular variation. Applications to compound distributions in insurance risk theory and queue length distributions under various queue disciplines in the case of Poisson arrivals are then discussed.
A Note on a Sample-Path Rate Conservation Law and its Relationship withH=λG
Authors: Sigman Karl
Published: April 2006

We present a simple sample-path version of the rate conservation law (of Miyazawa) and then show that theH=λGlaw (of Heyman and Stidham) is essentially the same law, that is, either one can be derived from the other. As a final remark we illustrate the use of both laws jointly to quickly obtain a queueing result.
Convergence in mean of some characteristics of the convex hull
Authors: Brozius Henk
Published: April 2006

A sequence Xn, 1 of independent and identically distributed random vectors is considered. Under a condition of regular variation, the number of vertices of the convex hull of {X1, …, Xn} converges in distribution to the number of vertices of the convex hull of a certain Poisson point process. In this paper, it is proved without sharpening the conditions that the expectation of this number also converges; expressions are found for its limit, generalizing results of Davis et al. (1987). We also present some results concerning other quantities of interest, such as area and perimeter of the convex hull and the probability that a given point belongs to the convex hull.
Poisson functionals of Markov processes and queueing networks
Authors: Serfozo Richard F.
Published: April 2006

We present conditions under which a point process of certain jump times of a Markov process is a Poisson process. The central idea is that if the Markov process is stationary and the compensator of the point process in reverse time has a constant intensitya, then the point process is Poisson with ratea.A known example is that the output flow from anM/M/1 queueing system is Poisson. We present similar Poisson characterizations of more general marked point process functionals of a Markov process. These results yield easy-to-use criteria for a collection of such processes to be multivariate Poisson, compound Poisson, or marked Poisson with a specified dependence or independence. We discuss several applications for queueing systems with batch arrivals and services and for networks of queues. We also indicate how our results extend to functionals of non-Markovian processes.
The fork-join queue and related systems with synchronization constraints: stochastic ordering and computable bounds
Authors: Baccelli François , Makowski Armand M. , Shwartz Adam
Published: April 2006

A simple queueing system, known as the fork-join queue, is considered with basic performance measure defined as the delay between the fork and join dates. Simple lower and upper bounds are derived for some of the statistics of this quantity. They are obtained, in both transient and steady-state regimes, by stochastically comparing the original system to other queueing systems with a structure simpler than the original system, yet with identical stability characteristics. In steady-state, under renewal assumptions, the computation reduces to standard GI/GI/1 calculations and the bounds constitute a first sizing-up of system performance. These bounds can also be used to show that for homogeneous fork-join queue system under assumptions, the moments of the system response time grow logarithmically in the number of parallel processors provided the service time distribution has rational Laplace–Stieltjes transform. The bounding arguments combine ideas from the theory of stochastic ordering with the notion of associated random variables, and are of independent interest to study various other queueing systems with synchronization constraints. The paper is an abridged version of a more complete report on the matter [6].
Maximization of availability of 1-out-of-2:G repairable dependent system
Authors: Joshi B. H. , Dharmadhikari A. D.
Published: April 2006

The IFR property of the stochastic process governing a one-component system supported by an inactive standby and a repair facility when the lifetime of one component and the repair time of the other component are dependent, is established. We solve the problem of selecting repair rates to maximize the steady-state availability for given component failure rates when a lower bound for the MTBF and upper bounds for the steady-state expected number of repairs of the components per unit time and expected number of failures of the system per unit time are given.
Improved Poisson approximations for word patterns
Authors: Godbole Anant P. , Schaffner Andrew A.
Published: April 2006

LetX1,X2,· ··, Xnbe a sequence ofnrandom variables taking values in theξ-letter alphabet. We consider the numberN = N(n, k) of non-overlapping occurrences of a fixedk-letter word under (a) i.i.d. and (b) stationary Markovian hypotheses on the sequence, and use the Stein–Chen method to obtain Poisson approximations for the same. In each case, results and couplings from Barbour et al. (1992) are used to show that the total variation distance between the distribution ofNand that of an appropriate Poisson random variable is of order (roughly)O(kS(k)), whereS(k)denotes the stationary probability of the word in question. These results vastly improve on the approximations obtained in Godbole (1991). In the Markov case, we also make use of recently obtained eigenvalue bounds on convergence to stationarity due to Diaconis and Stroock (1991) and Fill (1991).
The convex hull of random balls
Authors: Affentranger Fernando , Dwyer Rex A.
Published: April 2006

While the convex hull of n d-dimensional balls is not a polytope, it does have an underlying combinatorial structure similar to that of a polytope. In the worst case, its combinatorial complexity can be of order Ω(n[d/2]). The thrust of this work is to show that its complexity is typically much smaller, and that it can therefore be constructed more quickly on average than in the worst case. To this end, four models of the random d-ball are developed, and the expected combinatorial complexity of the convex hull of n independent random d-balls is investigated for each. As n grows without bound, these expectations are O(1), O(n(d–1)/(d+4)), O(1) (for d = 2 only), and O(n(d–1)/(d+3)).
Limit theorems for convex hulls of random sets
Authors: Molchanov Ilya S.
Published: April 2006

Let, be i.i.d. random closed sets in. Limit theorems for their normalized convex hullsconv () are proved. The limiting distributions correspond toC-stable random sets. The random closed setAis called C-stable if, for any, the setsanAand conv (coincide in distribution for certain positivean,compactKn, and independent copiesA1, …,AnofA.The distributions ofC-stable sets are characterized via corresponding containment functionals.
Event and time averages: a review
Authors: Brémaud Pierre , Kannurpatti Raghavan , Mazumdar Ravi
Published: April 2006

This article reviews results related to event and time averages (EATA) for point process models, including PASTA, ASTA and ANTIPASTA under general hypotheses. In particular, the results for the stationary case relating the Palm and martingale approach are reviewed. The non-stationary case is discussed in the martingale framework where minimal conditions for ASTA generalizing earlier work are presented in a unified framework for the discrete- and continuous-time cases. In addition, necessary and sufficient conditions for ASTA to hold in the stationary case are discussed in the case even when stochastic intensities may not exist and a short proof of the ANTIPASTA results known to date are given.
Limit theorems for the numbers of rare mutants: a branching process model
Authors: Pakes Anthony G.
Published: April 2006

We generalize a two-type mutation process in which particles reproduce by binary fission, inheriting the parental type, but which can mutate with small probability during their lifetimes to the opposite type. The generalization allows an arbitrary offspring distribution. The branching process structure of this scheme is exploited to obtain a variety of limit theorems, some of which extend known results for the binary case. In particular, practically usable asymptotic normality results are obtained when the initial population size is large.