bluuebunny/crossref_metadata_2025 huggingface dataset:
Sulphuryl fluoride fumigation: effect on DNA extraction and amplification from herbarium specimens
Authors: Whitten W. Mark , Williams Norris H. , Glover Kenneth V.
Published: April 2006

Whitten, W. M., Williams, N. H. & Glover, K. V.: Sulphuryl fluoride fumigation: effect on DNA extraction and amplification from herbarium specimens. – Taxon 48: 507‐510. 1999. – ISSN 0040‐0262.

Dried leaf samples were exposed to sulphuryl fluoride (Vikane) during herbarium fumigation. DNA was extracted from fumigated leaf samples and from unfumigated controls. Both fumigated and control samples yielded good quality DNA; DNA amplification yielded similar products from both sets of samples. Vikane does not appear to degrade DNA present in herbarium specimens, and appears to be a non‐destructive fumigant for pest control in herbaria.
Further results for Gauss-Poisson processes
Authors: Milne R. K. , Westcott M.
Published: April 2006

Newman (1970) introduced an interesting new class of point processes which he called Gauss-Poisson. They are characterized, in the most general case, by two measures. We determine necessary and sufficient conditions on these measures for the resulting point process to be well defined, and proceed to a systematic study of its properties. These include stationarity, ergodicity, and infinite divisibility. We mention connections with other classes of point processes and some statistical results. Our basic approach is through the probability generating functional of the process.
Inferences in the location of polygenes
Authors: Robertson Alan
Published: April 2006

In the location of genes affecting quantitative characters in Drosophila, Thoday has made extensive use of a technique of examining the products of crossovers between tester chromosomes and those from selected lines. The paper considers the validity of inferences which can be drawn from such experiments. The multiplicity of possible models makes this difficult and some efforts have been made, simulating results from given known situations. It seems probable that the shape of the final conclusions would be in terms of the power of the method to discover groups of genes, covering a certain length of chromosome and with a given sum total of effects.
The two locus model by different recombination values in the two sexes
Authors: Strobeck Curtis
Published: April 2006

In the two locus theory that has been developed, it has been assumed that amount of recombination between the two loci is the same in both sexes (Bodmer and Felsenstein, (1967); Karlin and Feldman, (1970)). Some results of assuming that the recombination value in males isrmand in femalesrfare reported here.
Optimal control of stochastic Ito differential systems by fixed terminal time
Authors: Ahmed N. U. , Teo K. L.
Published: April 2006

In this paper, the authors consider a class of stochastic systems described by Ito differential equations for which both controls and parameters are to be chosen optimally with respect to a certain performance index over a fixed time interval. The controls to be optimized depend only on partially observed current states as in a work of Fleming. However, he considered, instead, a problem of optimal control of systems governed by stochastic Ito differential equations with Markov terminal time. The fixed time problems usually give rise to the Cauchy problems (unbounded domain) whereas the Markov time problems give rise to the first boundary value problems (bounded domain). This fact makes the former problems relatively more involved than the latter. For the latter problems, Fleming has reported a necessary condition for optimality and an existence theorem of optimal controls. In this paper, a necessary condition for optimality for both controls and parameters combined together is presented for the former problems.
Ergodic theorems for graph interactions
Authors: Griffeath David
Published: April 2006

A criterion for ergodicity of lattice interactions has been given by Dobrushin [2], and improved by Harris [3] and Holley [5]. In this paper we present a simplified derivation of these results, and obtain stronger conditions for interactions on the one- and two-dimensional integer lattices, and the 3–Bethe lattice.
Vector linear time series models
Authors: Dunsmuir W. , Hannan E. J.
Published: April 2006

This paper presents proofs of the strong law of large numbers and the central limit theorem for estimators of the parameters in quite general finite-parameter linear models for vector time series. The estimators are derived from a Gaussian likelihood (although Gaussianity is not assumed) and certain spectral approximations to this. An important example of finite-parameter models for multiple time series is the class of autoregressive moving-average (ARMA) models and a general treatment is given for this case. This includes a discussion of the problems associated with identification in such models.
Discrete time methods for simulating continuous time Markov chains
Authors: Hordijk Arie , Iglehart Donald L. , Schassberger Rolf
Published: April 2006

This paper discusses several problems which arise when the regenerative method is used to analyse simulations of Markov chains. The first problem involves calculating the variance constant which appears in the central limit theorem used to obtain confidence intervals. Knowledge of this constant is very helpful in evaluating simulation methodologies. The second problem is to devise a method for simulating continuous time Markov chains without having to generate exponentially distributed holding times. Several methods are presented and compared. Numerical examples are given to illustrate the computional and statistical efficiency of these methods.
On the use of a fundamental identity in the theory of semi-Markov queues
Authors: Arjas E.
Published: April 2006

In the paper a single server semi-Markov queue is considered. The analysis is based on a fundamental matrix identity due to H. D. Miller. A natural method for the solution of semi-Markov queues is indicated; use is also made of a duality relation, which is discussed in the paper.
Stability of maxima of random variables defined on a Markov chain
Authors: Resnick Sidney I.
Published: April 2006

Consider maxima Mn of a sequence of random variables defined on a finite Markov chain. Necessary and sufficient conditions for the existence of normalizing constants Bn such that are given. The problem can be reduced to studying maxima of i.i.d. random variables drawn from a finite product of distributions πi=1mHi(x). The effect of each factor Hi(x) on the behavior of maxima from πi=1mHi is analyzed. Under a mild regularity condition, Bn can be chosen to be the maximum of the m quantiles of order (1 - n-1) of the H's.
Rates of convergence for queues in heavy traffic. I
Authors: Kennedy Douglas P.
Published: April 2006

Estimates are given for the rates of convergence in functional central limit theorems for quantities of interest in the GI/G/1 queue and a general multiple channel system. The traffic intensity is fixed ≧ 1. The method employed involves expressing the underlying stochastic processes in terms of Brownian motion using the Skorokhod representation theorem.
Optimal stationary policies for denumerable Markov chains in continuous time
Authors: Bather John
Published: April 2006

This paper is concerned with the problem of selecting the transition intensities for a Markov chain in continuous time so as to minimise the long-term average cost. Sufficient conditions are established for an optimal stationary policy using unbounded solutions of the optimality equation. This is a development of recent work on Markovian decision processes in discrete time. The theory is illustrated by considering a simple birth and death process with controlled immigration.
Generalized Gibbs states and Markov random fields
Authors: Preston C. J.
Published: April 2006

It is shown that the set of Markov random fields and Gibbs states with nearest neighbour potentials are the same for any finite graph. The set of Markov random fields is also shown to be the same as the equilibrium states of time-reversible birth/death processes with nearest neighbour interactions defined on the graph.
Optimal decision procedures for finite markov chains. Part I: Examples
Authors: Bather John
Published: April 2006

A Markov process in discrete time with a finite state space is controlled by choosing the transition probabilities from a prescribed set depending on the state occupied at any time. Given the immediate cost for each choice, it is required to minimise the expected cost over an infinite future, without discounting. Various techniques are reviewed for the case when there is a finite set of possible transition matrices and an example is given to illustrate the unpredictable behaviour of policy sequences derived by backward induction. Further examples show that the existing methods may break down when there is an infinite family of transition matrices. A new approach is suggested, based on the idea of classifying the states according to their accessibility from one another.
Asymptotic inference for an ising lattice. II
Authors: Pickard D. K.
Published: April 2006

In Pickard (1976) limit theorems were obtained for the classical Ising model at non-critical points. These determined the asymptotic distribution of the sample nearest-neighbour correlation, thereby providing a basis for statistical inference by confidence intervals. In this paper, these limit theorems are extended to the statistically significant case of different vertical and horizontal interactions. Results at critical points are also obtained. Critical points clearly have the potential to seriously distort statistical inferences, especially in their immediate neighbourhoods. For our Ising model it turns out that such distortion is relatively minor. Surprisingly, in the two-parameter case the correlation between the sufficient statistics exhibits peculiar asymptotic behaviour resulting in a singular covariance matrix at critical points in the central limit theorem. Finally, at critical points, unusual norming constants are required for the central limit theorem, and our results are much more sensitive to the relative rate at which m, n tend to infinity.
The M/G/1 queue with several types of customers and change-over times
Authors: Neuts Marcel F.
Published: April 2006

We study an M/G/1 queue with m types of customer, operating under the first-come, first-served discipline. It is assumed that the server expends a random length of time in change-over from one type of customer to another. Various priority rules have been proposed to reduce the amount of time spent in change-over. These queue disciplines generally require a separate monitoring, whose cost is frequently non-negligible. As a basis for evaluating the merits of alternate queue disciplines, it is important to have information on the M/G/1 queue with m customer types when service is first-come, first-served. By appealing to general methods for the M/SM/1 queue, a large number of detailed and explicit results are obtained. In addition, algorithmic solutions are given for the steady-state distributions which are analytically intractable.
Asymptotic behaviour of immigration-branching processes by general set of types. II: Supercritical branching part
Authors: Hering H.
Published: April 2006

We construct an immigration-branching process from an inhomogeneous Poisson process, a parameter-dependent probability distribution of populations and a Markov branching process with homogeneous transition function. The set of types is arbitrary, and the parameter is allowed to be discrete or continuous. Assuming a supercritical branching part with primitive first moments and finite second moments, we prove propositions on the mean square convergence and the almost sure convergence of normalized averaging processes associated with the immigration-branching process.
Estimation of embedded particle properties from plane section intercepts
Authors: Evans D. A. , Clarke K. R.
Published: April 2006

Estimation of the properties of particles embedded in a solid medium via observations on random plane sections is studied. The particular properties considered are those associated with steel inclusions, for example, projected area fraction, total caliper length per unit volume and elongation factor. The approach is general, and with the minimum of assumptions about the particle shape, formulae are obtained for suitable estimators and their variances. Generalised moment relations are derived for the case of given, arbitrary shapes. Estimations of the density of particle centres based upon reciprocal observations are shown to lack robustness to small changes in shape and a more reliable density estimator is discussed. Consideration is given to the case of particles with elliptical profiles and to the use of aggregated results which arise when using automatic scanning equipment. Results are given for the case when there is length-biassing of the intercept distribution due to edge-effects for finite sample areas. Finally, the implication of a positive lower resolution point is discussed.
Some exact distributions in traffic noise theory
Authors: Marcus Allan H.
Published: April 2006

The moment-generating function of the traffic noise from a stream of vehicles with identical noise emissions cannot be readily inverted. If the emissions are not equal, this generating function can be inverted to obtain the exact form of the distribution function in some particular cases. Noise intensity has a maximally skew stable distribution with exponent 1/2 for observers on the highway, whatever the distribution of emissions. The distribution at any distance from the highway is an exponentially modified stable law with exponent 1/2 for an improper exponential distribution of emissions, and an infinite series involving this stable law and iterated error functions when emissions have an exponential distribution. A doubly stochastic process for emissions produces distributions of traffic noise intensity in the domain of attraction of skew stable laws with exponent α, 1/2 < α < 2. The inverse Gaussian (exponentially modified skew stable law with exponent 1/2) is recommended as the best choice of a two-parameter family for fitting traffic noise intensity distributions.
Some results about Markov processes on subsets of the state space
Authors: Gzyl Cristina
Published: April 2006

Kingman [5] proved a formula that expresses the joint distribution of the processes

where b is a regular point in the state space of a Hunt process. We give an extension of this formula, as well as several interesting facts related to it, for the case when Φ is any finely perfect subset of the state space. We also establish some connections between this result and results on last-exit decompositions.
Limit theorems for α-recurrent semi-Markov processes
Authors: Nummelin Esa
Published: April 2006

In this paper the limit behaviour of α-recurrent Markov renewal processes and semi-Markov processes is studied by using the recent results on the concept of α-recurrence for Markov renewal processes. Section 1 contains the preliminary results, which are needed later in the paper. In Section 2 we consider the limit behaviour of the transition probabilities Pij(t) of an α-recurrent semi-Markov process. Section 4 deals with quasi-stationarity. Our results extend the results of Cheong (1968), (1970) and of Flaspohler and Holmes (1972) to the case in which the functions to be considered are directly Riemann integrable. We also try to correct the errors we have found in these papers. As a special case from our results we consider continuous-time Markov processes in Sections 3 and 5.
Networks of queues and the method of stages
Authors: Barbour Andrew D.
Published: April 2006

In a recent article, Kelly [4] has been able to exhibit interesting equilibrium properties for a wide class of ‘quasi-reversible’ queue networks. The assumption of quasi-reversibility puts restrictions on queue discipline, but not on the distributions of the service requirements of customers: however, because of the method of proof he employed, Kelly was forced to impose the condition that the service requirements were finite mixtures of gamma distributions. The form of the results he obtained led him to conjecture that this condition was in fact unnecessary, as is shown to be the case in this paper. The method used to prove the conjecture is of potentially wide application, in problems where the ‘method of stages' leads to useful simplification.
Structural models in epidemiology: an introductory investigation
Authors: Tautu Petre
Published: April 2006

The purpose of this paper is to bring to the attention of epidemiologists the possibility of setting up and utilizing structural models, more precisely, mathematical models based on graph theory. We shall present the first general results in this investigation using some statements and definitions.
The estimation of parameters from population data on the general stochastic epidemic
Authors: Bailey Norman T. J. , Thomas Anthony S.
Published: April 2006

We consider the usual stochastic model of a general epidemic, consisting of n + 1 homogeneously mixing individuals, assuming that initially when t = 0 there is one infective and n susceptibles (Bailey (1957)). At any time t we suppose that there are r susceptibles still uninfected, s infectives in circulation, and u individuals who have been removed (and are dead, isolated, or recovered and immune), where
On a perturbation method for the theory of epidemics
Authors: Weiss George H.
Published: April 2006

The theory of epidemics has been formulated as a deterministic theory and as a stochastic theory. There has been little work, except for a recent paper by Bailey [1], on the transition between the two formulations. In this paper we present an alternate formulation to that of Bailey that leads to a perturbation method more easily extendible to higher orders.
Asymptotic methods for problems in the mathematical theory of epidemics
Authors: Nagaev A. V.
Published: April 2006

Let n and m be the initial numbers of susceptibles and infectives respectively in the well-known model of Bailey. The successive states of a population will be described by (i,j), where i is the number infected since the beginning of the epidemic, and j is the number removed (dead, isolated or recovered and immune) during the same period. The transition probabilities obviously are the following
Joint distributions of random variables and their integrals for certain birth-death and diffusion processes
Authors: Gani J. , Mcneil D. R.
Published: April 2006

For the linear growth birth-death process with parameters λn=nλ, μn=nμ, Puri ((1966), (1968)) has investigated the joint distribution of the numberX(t) of survivors in the process and the associated integralY(t) = ∫0tX(τ)dτ. In particular, he has obtained limiting results ast→ ∞. Recently one of us (McNeil (1970)) has derived the distribution of the integral functionalWx= ∫0Txg{X(τ)}dτ, whereTxis the first passage time to the origin in a general birth-death process withX(0) =xandg(·) is an arbitrary function. Functionals of the formWxarise naturally in traffic and storage theory; for exampleWxmay represent the total cost of a traffic jam, or the cost of storing a commodity until expiration of the stock. Moments of such functionals were found in the case ofM/G/1 andGI/M/1 queues by Gaver (1969) and Daley (1969).
The maximum size of a closed epidemic
Authors: Daniels H. E.
Published: April 2006

An approximation is found to the distribution of the maximum number of infectives present at any time during the course of a closed epidemic. The technique used is applicable to a commonly occurring type of random walk problem where there is a curved absorbing boundary which is far from the mean path except over a narrow range.
Optimal control of finite dams: continuous output procedure
Authors: Faddy M. J.
Published: April 2006

The problem discussed is that of controlling optimally the release of water from a finite dam, when the release rate may vary continuously and the optimality is defined in terms of a cost structure imposed on the operation of the dam. A diffusion model is suggested and by considering a family of plausible output policies, the control problem is reduced to the solution of a free boundary problem associated with a certain partial differential equation. A set of necessary conditions for the optimal choice of these boundaries is established and a method of solution is suggested. By using this method, together with well-established computational techniques, numerical solutions are obtained. These numerical solutions indicate that this optimal policy does not result in very much improvement over a much simpler policy where the output rate is constrained to take only two values.
Asymptotic properties of supercritical branching processes I: The Galton-Watson process
Authors: Bingham N. H. , Doney R. A.
Published: April 2006

We obtain results connecting the distributions of the random variables Z1 and W in the supercritical Galton-Watson process. For example, if a > 1, and converge or diverge together, and regular variation of the tail of one of Z1, W with non-integer exponent α > 1 is equivalent to regular variation of the tail of the other.
Searching for a particle on the real line
Authors: Fristedt Bert , Heath David
Published: April 2006

In this paper we consider two optimization problems and two game problems. In each problem, a particle is hidden on the real line (sometimes randomly, and sometimes by an antagonistic hider), and a seeker, starting at the origin, wishes to find the particle with minimal expected cost. We consider a fairly wide class of cost functions depending upon the position of the particle and the time used to discover it. For the games we obtain the values and (∊-) optimal strategies. For the optimization problems we obtain qualitative features of (∊-) optimal searches.
Approximations for the repairman problem with two repair facilities, II: Spares
Authors: Iglehart Donald L. , Lemoine Austin J.
Published: April 2006

The model considered here consists of n operating units which are subject to stochastic failure according to an exponential failure time distribution. These operating units are backed up by mn spare units. Failures can be of two types. With probability p (q) a failure is of type 1(2) and is sent to repair facility 1(2) for repair. Repair facility 1(2) operates as a -server queue with exponential repair times having parameter μ1 (μ2). The number of units waiting for or undergoing repair at each of the two facilities is a continuous parameter Markov chain with finite state space. This paper derives limit theorems for the stationary distribution of this Markov chain as n becomes large under the assumption that and mn grow linearly with n. These limit theorems give very useful approximations, in terms of the seven parameters characterizing the model, to a distribution that would be difficult to calculate in practice.
Limit theorems for generalized single server queues
Authors: Lemoine Austin J.
Published: April 2006

For the generalized single server queueing system described herein weak convergence results are obtained for the processes {Wa, n ≧ 0}, {W(t), t ≧ 0}, and {Q (t), t ≧ 0}, where Wn is the waiting time of customer n, W(t) is the workload of the server at time t, and Q(t) is the number of customers present in the system at time t. We also provide a functional strong law, a functional central limit theorem, and a functional law of the iterated logarithm for various cumulative processes in the system.
Poisson flats in Euclidean spaces Part I: A finite number of random uniform flats
Authors: Miles R. E.
Published: April 2006

This is the first part of a three part work, the common setting being Ed, Euclidean space of d dimensions. Many random physical phenomena, often in the form of structures, admit models which are assemblages of random s-flats in Ed. Indeed, taking s = 0, any n-sample from a d-dimensional distribution may of course be so regarded! For static phenomena generally 0 ≦ s < d ≦ 3, while 4 is to be substituted for 3 if time variation is allowed. By postulating a high degree of stochastic independence and uniformity, a variety of “simple” models is defined. However, their investigation poses problems in geometrical probability of a wide range of difficulty; the solutions of many of which are still far from complete.
On a conjecture of G. A. Watterson
Authors: Trajstman A. C.
Published: April 2006

It is shown that two different population models are equivalent to each other when a certain marginal stationary distribution is considered.
Properties and applications of stochastic processes with stationarynth-order increments
Authors: Picinbono B.
Published: April 2006

Many physical problems are described by stochastic processes with stationary increments. We present a general description of such processes. In particular we give an expression of a process in terms of its increments and we show that there are two classes of processes: diffusion and asymptotically stationary. Moreover, we show that thenth increments are given by a linear filtering of an arbitrary stationary process.
Renewal theory in two dimensions: asymptotic results
Authors: Hunter Jeffrey J.
Published: April 2006

In an earlier paper (Renewal theory in two dimensions: Basic results) the author developed a unified theory for the study of bivariate renewal processes. In contrast to this aforementioned work where explicit expressions were obtained, we develop some asymptotic results concerning the joint distribution of the bivariate renewal counting process (Nx(1),Ny(2)), the distribution of the two-dimensional renewal counting processNx,yand the two-dimensional renewal function &Nx,y. A by-product of the investigation is the study of the distribution and moments of the minimum of two correlated normal random variables. A comprehensive bibliography on multi-dimensional renewal theory is also appended.
Hyperplans poissoniens et compacts de Steiner
Authors: Matheron G.
Published: April 2006

A compact convex set in RN is Steiner if it is a finite Minkowski sum of line segments, or a limit of such finite sums, and then satisfies an extension of the Steiner formula. With each Poisson hyperplane stationary process A is uniquely associated a Steiner set M, and for any linear variety V, the Steiner set associated with is the projection of M on V. The density of the order k network Ak (i.e., the set of the intersections of k hyperplanes belonging to A) is linked with simple geometrical properties of M. In the isotropic case, the expression of the covariance measures associated with Ak is derived and compared with the analogous results obtained for (N — k)-dimensional Poisson flats.
Stepping stone models of finite length
Authors: Maruyama Takeo
Published: April 2006

The stepping stone model of population structure, of finite length, is analysed with special reference to the variance, and correlation coefficients of gene frequencies. Explicit formulas for these quantities are obtained. The model is also analysed for the genetic variability maintained in the population. In order to check the validity of the analytical results, several numerical computations were carried out using two different methods: iterations and Monte Carlo experiments. The values obtained by these numerical methods agree well with the theoretical values obtained by formulas derived analytically.
On the distribution of the maximum of sums of mutually independent and identically distributed random variables
Authors: Takács Lajos
Published: April 2006

Throughout this paper we shall be concerned with a sequence of mutually independent and identically distributed random variables ξ1 ξ2, · · ·, ξn, · · · taking on real values. We shall use the notation ζn = ξ1 + · · · + ξn for n = 1, 2, · · · and ζ0 = 0.
The probabilities of rooted tree-shapes generated by random bifurcation
Authors: Harding E. F.
Published: April 2006

The set of rooted trees, generated by random bifurcation at the terminal nodes, is considered with the aims of enumerating it and of determining its probability distribution. The account of enumeration collates much previous work and attempts a complete perspective of the problems and their solutions. Asymptotic and numerical results are given, and some unsolved problems are pointed out. The problem of ascertaining the probability distribution is solved by obtaining its governing recurrence equation, and numerical results are given. The difficult problem of determining the most probable tree-shape of given size is considered, and for labelled trees a conjecture at its solution is offered. For unlabelled shapes the problem remains open. These mathematical problems arise in attempting to reconstruct evolutionary trees by the statistical approach of Cavalli-Sforza and Edwards.
The geometry of random drift II. The symmetry of random genetic drift
Authors: Antonelli Peter L. , Chapin Jared , Lathrop G. Mark , Morgan Kenneth
Published: April 2006

It has been conjectured that a certain transformation of gene frequency space due to Fisher and Bhattacharyya will map the random genetic drift process, or its diffusion approximation, into one with radial symmetry. This paper proves rigorously that the Fisher–Bhattacharyya mapping does not do this. This implies that the initial state of an evolving ensemble can only be unbiasedly estimated from the means of a sample if we weight by the proper divergence times. If the ensemble is known not to have begun at the centroid of frequency space, the estimate of the initial state vector is not simply the arithmetic average, as symmetry analysis of the Christoffel velocity field shows.
A general markov decision method II: Applications
Authors: De Leve G. , Federgruen A. , Tijms H. C.
Published: April 2006

In a preceding paper [2] we have introduced a new approach for solving a wide class of Markov decision problems in which the state-space may be general and the system may be continuously controlled. The criterion is the average cost. This paper discusses two applications of this approach. The first application concerns a house-selling problem in which a constructor builds houses which may be sold at any stage of the construction and potential customers make offers depending on the stage of the construction. The second application considers an M/M/c queueing problem in which the number of operating servers can be controlled by turning servers on or off.
Processus ponctuels et martingales: résultats récents sur la modélisation et le filtrage
Authors: Brémaud P. , Jacod J.
Published: April 2006

This paper contains a review of the results of the martingale approach to point processes and its applications to the theory of dynamical systems (in the engineering sense), mainly estimation problems.

Some of the topics reviewed are: stochastic intensity, absolutely continuous changes of measure, martingale representations, changes of times, filtering, queues, etc.
Direct derivations of certain surface integral formulae for the mean projections of a convex set
Authors: Miles R. E.
Published: April 2006

A simple direct proof is given of Minkowski's result that the mean length of the orthogonal projection of a convex set in E3 onto an isotropic random line is (2π)–1 times the integral of mean curvature over its surface. This proof is generalised to a correspondingly direct derivation of an analogous formula for the mean projection of a convex set in En onto an isotropic random s-dimensional subspace in En. (The standard derivation of this, and a companion formula, to be found in Bonnesen and Fenchel's classic book on convex sets, is most indirect.) Finally, an alternative short inductive derivation (due to Matheron) of both formulae, by way of Steiner's formula, is presented.
A storage process by semi-Markov input
Authors: Takács Lajos
Published: April 2006

A sequence of random variables η0, η1, …, ηn, … is defined by the recurrence formula ηn = max (ηn–1 + ξn, 0) where η0 is a discrete random variable taking on non-negative integers only and ξ1, ξ2, … ξn, … is a semi-Markov sequence of discrete random variables taking on integers only. Define Δ as the smallest n = 1, 2, … for which ηn = 0. The random variable ηn can be interpreted as the content of a dam at time t = n(n = 0, 1, 2, …) and Δ as the time of first emptiness. This paper deals with the determination of the distributions of ηn and Δ by using the method of matrix factorisation.
Estimation de l'État d'une file d'attente et du temps de panne d'une machine par la méthode de semi-martingales
Authors: Brémaud P.
Published: April 2006

We establish the estimation equations corresponding to a system in which the state is a process with jumps and the observation is a point process. We then solve two problems: the estimation of the state of a queue when its output is observed, and the estimation of the time of disorder of a machine when the ‘complaints process’ is observed.
Approximation of the invariant probability measure of an infinite stochastic matrix
Authors: Wolf D.
Published: April 2006

Let P denote an irreducible positive recurrent infinite stochastic matrix with the unique invariant probability measure π. We consider sequences {Pm}m∊N of stochastic matrices converging to P (pointwise), such that every Pm has at least one invariant probability measure πm. The aim of this paper is to find conditions, which assure that at least one of sequences {πm}m∊N converges to π (pointwise). This includes the case where the Pm are finite matrices, which is of special interest. It is shown that there is a sequence of finite stochastic matrices, which can easily be constructed, such that {πm}m∊N converges to π. The conditions given for the general case are closely related to Foster's condition.
First-order autoregressive gamma sequences and point processes
Authors: Gaver D. P. , Lewis P. A. W.
Published: April 2006

It is shown that there is an innovation process {∊n} such that the sequence of random variables {Xn} generated by the linear, additive first-order autoregressive schemeXn=pXn-1+ ∊nare marginally distributed as gamma (λ,k) variables if 0 ≦p≦ 1. This first-order autoregressive gamma sequence is useful for modelling a wide range of observed phenomena. Properties of sums of random variables from this process are studied, as well as Laplace-Stieltjes transforms of adjacent variables and joint moments of variables with different separations. The process is not time-reversible and has a zero-defect which makes parameter estimation straightforward. Other positive-valued variables generated by the first-order autoregressive scheme are studied, as well as extensions of the scheme for generating sequences with given marginal distributions and negative serial correlations.
Limit theorems and approximations for the reliability of load-sharing systems
Authors: Smith Richard L.
Published: April 2006

Techniques for studying the reliability of simple series or parallel systems are well known. This paper is concerned with more complicated systems in which the load on failed elements is transmitted to unfailed elements according to some load-sharing rule. The emphasis is on local load sharing, and in particular on a specific load-sharing rule introduced by Harlow and Phoenix for fibrous composites. Earlier results are reviewed and improved techniques for approximating the probability of failure and the size effect are derived.
On the limiting distribution of the failure time of fibrous materials
Authors: De Souza Borges Wagner
Published: April 2006

A large deviation theorem of the Cramér–Petrov type and a ranking limit theorem of Loève are used to derive an approximation for the statistical distribution of the failure time of fibrous materials. For that, fibrous materials are modeled as a series of independent and identical bundles of parallel filaments and the asymptotic distribution of their failure time is determined in terms of statistical characteristics of the individual filaments, as both the number of filaments in each bundle and the number of bundles in the chain grow large simultaneously. While keeping the number n of filaments in each bundle fixed and increasing only the chain length k leads to a Weibull limiting distribution for the failure time, letting both increase in such a way that log k(n) = o(n), we show that the limit distribution is for . Since fibrous materials which are both long and have many filaments prevail, the result is of importance in the materials science area since refined approximations to failure-time distributions can be achieved.
On the GA/G/∞ queue
Authors: Kuczek Thomas
Published: April 2006

A particular queue, the general arrival, general service-time, infinite-server queue (GA/G/∞), is introduced and certain of its properties studied. Motivated by a life situation in which the interarrival times for service converge to 0, a different sort of regularity condition (involving a tail property of random measures) is imposed on the arrival process to prove various limit theorems. There are similarities to heavy-traffic theory.
Optimal control of random walks, birth and death processes, and queues
Authors: Serfozo Richard
Published: April 2006

This is a study of simple random walks, birth and death processes, and M/M/s queues that have transition probabilities and rates that are sequentially controlled at jump times of the processes. Each control action yields a one-step reward depending on the chosen probabilities or transition rates and the state of the process. The aim is to find control policies that maximize the total discounted or average reward. Conditions are given for these processes to have certain natural monotone optimal policies. Under such a policy for the M/M/s queue, for example, the service and arrival rates are non-decreasing and non-increasing functions, respectively, of the queue length. Properties of these policies and a linear program for computing them are also discussed.
Regeneration in tandem queues
Authors: Nummelin E.
Published: April 2006

Consider a tandem queue with renewal input process and i.i.d. service times (at each server). This paper is concerned with the construction of regeneration times for the multivariate Markov chain formed by the interarrival times, waiting times and service times of the customers.
How Evolutionarily Stable is the Xx/Xy Sex-Determination System?
Authors: Bengtsson Bengt O.
Published: April 2006

The sex of a zygote is often decided by an XX/XY sex-determination mechanism. One important property of this system is the approximate numerical equality of the two sexes (at least at fertilization) due to mendelian segregation. Does the obvious evolutionary stability of the XX/XY sex-determination system pose a difficult problem to population genetics? We study the fate of new mutations occurring in populations with an XX/XY system, where the mutations are such that they change the sex-determination system. If such mutations occur frequently and the conditions for their initial increase are weak, then the evolutionary stability of the XX/XY system is hard to understand.
The behaviour of strategy-frequencies in Parker's model
Authors: Gardiner D.
Published: April 2006

Parker's model (or the Scotch Auction) for a contest between two competitors has been studied by Rose (1978). He considers a form of the model in which every pure strategy is playable, and shows that there is no evolutionarily stable strategy (ess). In this paper, in order to discover more about the behaviour of strategies under the model, we shall assume that there are only a finite number of playable pure strategies I1, I2, ···, In where Ij is the strategy ‘play value mj′ and m1 < m2 < ··· < mn. The payoff matrix A for the contest is then given by

where V is the reward for winning the contest, C is a constant added to ensure that each entry in A is non-negative (see Bishop and Cannings (1978)), and E[Ii, Ij] is the expected payoff for playing Ii against Ij. We also assume that A is regular (Taylor and Jonker (1978)) i.e. that all its rows are independent.
The algebraic approach to Bernstein's problem on Mendelian models of inheritance
Authors: Odoni R. W. K.
Published: April 2006

Consider a single gene locus for which the associated character is not sex-linked, and suppose that the character is exhibited as one of alleles. Under the Mendelian model of inheritance, if genotype frequencies are constant, the distribution of zygotes is stable from the second generation on, regardless of the value of n. (This is the celebrated Hardy–Weinberg law—see Hardy (1908).) In 1924 Bernstein raised the question of whether the Mendelian model is, in fact, a necessary consequence of the assumption that the zygote distribution is stable from the second generation on; when n = 2 or 3 Bernstein gave an affirmative solution, using elementary but tedious manipulation of probabilities. Lyubich (1971) used methods of convex analysis to obtain a partial solution of Bernstein's problem for general n. Holgate (1975) introduced algebraic methods in order to present a clearer picture of the underlying structures, and to relate Bernstein's problem to the algebras studied by Etherington (1939), Schafer (1949) and others. The purpose of this paper is to expound recent work of the author and others, building on Holgate's and Lyubich's ideas. The subject-matter of the paper is contained in a forthcoming joint paper by the author and A. E. Stratton.
The coupling of regenerative processes
Authors: Thorisson Hermann
Published: April 2006

A distributional coupling concept is defined for continuous-time stochastic processes on a general state space and applied to processes having a certain non-time-homogeneous regeneration property: regeneration occurs at random times So, S1, · ·· forming an increasing Markov chain, the post-Sn process is conditionally independent of So, · ··, Sn–1 given Sn, and the conditional distribution is independent of n. The coupling problem is reduced to an investigation of the regeneration times So, S1, · ··, and a successful coupling is constructed under the condition that the recurrence times Xn+1 = Sn+1 – Sn given that , are stochastically dominated by an integrable random variable, and that the distributions , have a common component which is absolutely continuous with respect to Lebesgue measure (or aperiodic when the Sn's are lattice-valued). This yields results on the tendency to forget initial conditions as time tends to ∞. In particular, tendency towards equilibrium is obtained, provided the post-Sn process is independent of Sn. The ergodic results cover convergence and uniform convergence of distributions and mean measures in total variation norm. Rate results are also obtained under moment conditions on the Ps's and the times of the first regeneration.
Statistical spatial series modelling II: Some further results on unilateral lattice processes
Authors: Tjøstheim Dag
Published: April 2006

An asymptotic theory of estimation is developed for classes of spatial seriesF(x1, · ··,xn), where (x1, · ··,xn) varies over a regular cartesian lattice. Two classes of unilateral models are studied, namely half-space models and causal (quadrant-type) models. It is shown that a number of asymptotic results are common for these models. Of special interest for practical applications is the problem of determining how many parameters should be included to describe the degree of dependence in each direction. Here we are able to obtain weakly consistent generalizations of familiar time-series criteria under the assumption that the generating variables of the model are independently and identically distributed. For causal models we introduce the concepts of spatial innovation process and lattice martingale and use these to extend some of the asymptotic theory to the case where a certain type of dependence is permitted in the generating variables.
Sojourn times in closed queueing networks
Authors: Kelly F. P. , Pollett P. K.
Published: April 2006

This paper obtains the stationary joint distribution of a customer's sojourn times along an overtake-free path in a closed multiclass Jackson network. The distribution has a simple representation in terms of the product form distribution for the state of the network at an arrival instant.
Inventory systems of perishable commodities
Authors: Kaspi H. , Perry D.
Published: April 2006

This paper deals with the blood-bank model; namely, an inventory system in which both arrival of items and demand are stochastic and items stored have finite lifetimes. We assume that the arrival and demand processes are independent Poisson processes. We use an analogy with queueing models with impatient customers to obtain some of the important characteristics of the system.
An inventory system with both delayed and immediate delivery
Authors: Hovey Peter W. , Purdue Peter
Published: April 2006

An M/G/∞ queue that is cleared whenever the level Q is exceeded plays the role of the outstanding orders process in an inventory system. The stationary version of the process is examined and an interesting property of the variance is illustrated.
Models for binary directed graphs and their applications
Authors: Wasserman Stanley S.
Published: April 2006

The nature and historical development of both stochastic and deterministic models for binary graphs are discussed. Here the focus of applications is sociological and emphasizes representations of networks of interpersonal relations as directed graphs. Models from the natural sciences and from the social sciences are examined and suggestions for future research are given.
Group replacement of a multicomponent system which is subject to deterioration only
Authors: Sivazlian B. D. , Mahoney J. F.
Published: April 2006

The stationary characteristics of an n-component periodic review system which is subject to stochastic deterioration (but not to failure) are investigated. When the n-component vector which expresses the state of deterioration of the system pierces a certain surface the entire multicomponent system is replaced by items of identical cost structure at the time of the next review. In the absence of this situation nothing is replaced. It is assumed that there is a fixed cost associated with each replacement and that the operating cost of each item is a strictly increasing function of its state of deterioration. The conditions for minimizing the long-term cost of maintaining a system which operates under the stated policy were found through solution of a problem in variational calculus. Two examples are worked. A useful graph which aids in the solution of such problems is provided.
Wandering phenomena in infinite-allelic diffusion models
Authors: Shiga Tokuzo
Published: April 2006

We introduce a class of infinite-dimensional diffusion processes which contains a limiting version of the Ohta–Kimura model in population genetics. For this a necessary and sufficient condition for existence of stationary distributions is obtained. We are especially interested in the case where there is no stationary distribution. Then it is shown that an individual ergodic theorem holds for a suitably centralized process. As a corollary the wandering distribution exists.
Random variables with maximum sums
Authors: Rüschendorf Ludger
Published: April 2006

Motivated by a problem in PERT networks we consider the question of construction of random variables with maximum sums when the marginals are fixed.
The asymptotic shape of the branching random walk
Authors: Biggins J. D.
Published: April 2006

In a supercritical branching random walk on Rp, a Galton–Watson process with the additional feature that people have positions, let be the set of positions of the nth-generation people, scaled by the factor n–1. It is shown that when the process survives looks like a convex set for large n. An analogous result is established for an age-dependent branching process in which people also have positions. In certain cases an explicit formula for the asymptotic shape is given.
Approximate solution of random ordinary differential equations
Authors: Boyce William E.
Published: April 2006

This is a largely expository paper on approximate methods of solving random ordinary differential equations, with an emphasis on direct numerical methods. Two methods are discussed in some detail and several others are mentioned briefly.