bluuebunny/crossref_metadata_2025 huggingface dataset:
Portfolio choice and the Bayesian Kelly criterion
Authors: Browne Sid , Whitt Ward
Published: April 2006

We derive optimal gambling and investment policies for cases in which the underlying stochastic process has parameter values that are unobserved random variables. For the objective of maximizing logarithmic utility when the underlying stochastic process is a simple random walk in a random environment, we show that a state-dependent control is optimal, which is a generalization of the celebrated Kelly strategy: the optimal strategy is to bet a fraction of current wealth equal to a linear function of the posterior mean increment. To approximate more general stochastic processes, we consider a continuous-time analog involving Brownian motion. To analyze the continuous-time problem, we study the diffusion limit of random walks in a random environment. We prove that they converge weakly to a Kiefer process, or tied-down Brownian sheet. We then find conditions under which the discrete-time process converges to a diffusion, and analyze the resulting process. We analyze in detail the case of the natural conjugate prior, where the success probability has a beta distribution, and show that the resulting limit diffusion can be viewed as a rescaled Brownian motion. These results allow explicit computation of the optimal control policies for the continuous-time gambling and investment problems without resorting to continuous-time stochastic-control procedures. Moreover they also allow an explicit quantitative evaluation of the financial value of randomness, the financial gain of perfect information and the financial cost of learning in the Bayesian problem.
Inference on binary images from binary data
Authors: Glasbey C. A.
Published: April 2006

The problem addressed is to reverse the degradation which occurs when images are digitised: they are blurred, subjected to noise and rounding error, and sampled only at a lattice of points. Inference is considered for the fundamental case of binary scenes, binary data and isotropic blur. The inferential process is separable into two stages: first from the lattice points to a binary image in continuous space and then the reversal of thresholding and blur. Methods are motivated by, and illustrated using, an electron micrograph of an immunogold-labelled section of tulip virus.
General conditions for bounded relative error in simulations of highly reliable Markovian systems
Authors: Nakayama Marvin K.
Published: April 2006

We establish a necessary condition for any importance sampling scheme to give bounded relative error when estimating a performance measure of a highly reliable Markovian system. Also, a class of importance sampling methods is defined for which we prove a necessary and sufficient condition for bounded relative error for the performance measure estimator. This class of probability measures includes all of the currently existing failure biasing methods in the literature. Similar conditions for derivative estimators are established.
A revision of native Moroccan species of Lavandula L. section Pterostoechas Ging. (Lamiaceae)
Authors: Upson Tim M. , Jury Stephen L.
Published: April 2006

A revision of the eight native Moroccan species of Lavandula L. section Pterostoechas Ging., based on herbarium studies, SEM photographs, and field observations, is presented utilising morphological, phenological and ecological characters. Within Lavandula of Morocco, L. sect. Pterostoechas with six species is the most diverse, one of which is described here as new (L. rejdalii Upson & Jury). Four of these species are endemic: L. maroccana Murb., L. tenuisecta Coss. ex Ball, L. rejdalii Upson & Jury, and L. mairei Humbert [with two varieties, L. mairei var. mairei and L. mairei var. antiatlantica (Humbert) Maire]. The other two species, Lavandula multifida L. and L. coronopifolia Poir., are native but more widespread species. The distribution of the species in Morocco is shown in grid maps. Lavandula brevidens (Humbert) Maire and its infraspecific taxa are not retained, being reduced to synonymy under L. tenuisecta and L. rejdalii. Full synonymy is given for all taxa and names are lectotypified as necessary.
Unearthing a 19th century mycological treasure: discovery of the first edition of Fries’s Scleromyceti Sueciae in the Schweinitz Herbarium at PH
Authors: Untereiner Wendy A.
Published: April 2006

A search for Fries’s Scleromyceti Sueciae at the Academy of Natural Sciences of Philadelphia (PH) was initiated following the receipt of a specimen annotated “Suec. Fr.” from the Schweinitz Herbarium. Study of the collection of fungi at PH revealed 340 similarly annotated specimens, 76 printed labels from Fascicles 1–6, and 8 of the first edition of the Scleromyceti Sueciae, and a page of the index from Decade XXXI of Fascicle 9. In many cases, sheets from this exsiccata were folded inward to form packets that enclosed both the specimen and the printed label. This paper also reports the discovery of 21 specimens from the Deutschlands Schwämme at PH.
Yams reclassified: a recircumscription of Dioscoreaceae and Dioscoreales
Authors: Caddick Lizabeth R. , Wilkin Paul , Rudall Paula J. , Hedderson Terry A. J. , Chase Mark W.
Published: April 2006

Analyses of morphological and molecular characters for Dioscoreales Hook. f. (Chase & al., 1995b; Caddick & al., 2000a; Caddick & al., 2002) have redefined the order, which now comprises three families, Burmanniaceae, Dioscoreaceae, and Nartheciaceae. Since recent analyses of morphological and molecular data sets (Caddick & al., 2002) have indicated well­supported relationships within Dioscoreaceae R. Br., a formal reclassification of the family is presented here. Dioscoreaceae now contain four distinct genera,Dioscorea, Stenomeris, Tacca(previously in Taccaceae), andTrichopus. The Malagasy endemicAvetra sempervirensis close sister toTrichopus zeylanicus, and is here reclassified as a second species of this genus. The dioecious Dioscoreaceae genera,Borderea, Epipetrum, Nanarepenta, Rajania, Tamus, andTestudinaria, are nested withinDioscoreain phylogenetic analyses (Caddick & al., 2002), and are therefore sunk into it.
Some floristic characteristics of the northern Chihuahuan Desert: a search for its northern boundary
Authors: Muldavin Esteban H.
Published: April 2006

An index of Chihuahuan floristic affinity was constructed to characterize the floristic variation over a 5° latitudinal gradient in the northern Chihuahuan Desert, with an emphasis on evaluating northern boundary conditions. The index was based on evaluating the ranges of 494 species from 590 vegetation plots from Bouteloua eriopoda and B. gracilis grasslands and Larrea tridentata scrub, distributed among four sites along the gradient. The most northern site, the Sevilleta National Wildlife Refuge (34°N latitude), while maintaining a complement of primarily southern distributed species, had the lowest index values and the fewest Chihuahuan endemics (3%) and Southwestern desert species (19%) in general. At the intermediate sites (Jornada/Tularosa basins and Otero Mesa), one and two degrees further south, index values increased conspicuously along with number of Chihuahuan endemics (7%) and the Southwestern desert species (37%). At 29°N latitude, the Sierra del Carmen Protected Area in northern Mexico was the furthest southern site. It represented typical hot and dry Chihuahuan Desert conditions where Chihuahuan endemics comprised 29% of species complement and Southwestern desert species made up 55%. With respect to floristic boundaries, the Sevilleta was clearly transitional to the southern Shortgrass Prairie and Intermountain (Great Basin­Colorado Plateau) provinces. While it supported several grassland and shrubland associations that maintained their overall Chihuahuan character, there were also several associations with primarily northern affinities, and also a set unique to the Sevilleta, reflecting its ecotonal nature. The results show that sound biosystematics, biogeographical analyses and indices like those presented here can provide an important context for questions in synecology, plant ecology, and conservation biology.
On the single-server queue with non-homogeneous Poisson input and general service time
Authors: Hasofer A. M.
Published: April 2006

In this paper, a single-server queue with non-homogeneous Poisson input and general service time is considered. Particular attention is given to the case where the parameter of the Poisson input λ(t) is a periodic function of the time. The approach is an extension of the work of Takács and Reich . The main result of the investigation is that under certain conditions on the distribution of the service time, the form of the function λ(t) and the distribution of the waiting time at t = 0, the probability of a server being idle P0 and the Laplace transform Ω of the waiting time are both asymptotically periodic in t. Putting
where b(t) is a periodic function of time, it is shown that both Po and Ω can be expanded in a power series in z, and a method for calculating explicitly the asymptotic values of the leading terms is obtained.

In many practical queueing problems, it is expected that the probability of arrivals will vary periodically. For example, in restaurants or at servicestations arrivals are more probable at rush hours than at slack periods, and rush hours are repeated day after day
Fluctuations in the ratio of scores in counting a ballot
Authors: Takács Lajos
Published: April 2006

Suppose that in a ballot candidate A scores a votes and candidate B scores b votes and that all the possible voting records are equally probable. Denote by α r and β r, the number of votes registered for A and B respectively among the first r votes recorded. Let µ, be a nonnegative integer. Denote by Pj(a, b) the probability that the inequality holds for exactly j subscripts r=1,2,..,a + b.
Interval estimates of language divergence times
Authors: Dobson A. J.
Published: April 2006

It is often convenient to construct a branching diagram to represent the relationships between languages belonging to the same language family (for example, between Romance languages such as Rumanian, Italian, French and Spanish). It is desirable that the diagram should illustrate both the closeness of the relationships (that is, which pairs of languages have an immediate common ancestor and which are more remotely related) and the relative chronology of the languages. In this paper, the problem of estimating the time since two languages had a common ancestor and were the same is considered. Interval estimates are sought since, in general, consistent point estimates may be impossible; a numerical example is given to illustrate this.
A rate of convergence result for the super-critical Galton-Watson process
Authors: Heyde C. C.
Published: April 2006

Let Z0 = 1, Z1, Z2, ··· denote a super-critical Galton-Watson process whose non-degenerate offspring distribution has probability generating function where 1 < m = EZ1 < ∞. The Galton-Watson process evolves in such a way that the generating function Fn(s) of Znis the nth functional iterate of F(s). The convergence problem for Zn, when appropriately normed, has been studied by quite a number of authors; for an ultimate form see Heyde [2]. However, no information has previously been obtained on the rate of such convergence. We shall here suppose that in which case Wn = m –nZn converges almost surely to a non-degenerate random variable W as n → ∞ (Harris [1], p. 13). It is our object to establish the following result on the rate of convergence of Wn to W.
Two classification theorems of states of Markov chains
Authors: Kim C. W.
Published: April 2006

Two theorems on Markov chains, both of which already appear in the literature: the classification of the states into the set of all non-recurrent (transient) states and recurrent classes, and the corresponding classification for idempotent Markov chains due to Doob, are proved from the viewpoint of ergodic theory.
On the model of Weiss for the spread of epidemics by carriers
Authors: Dietz Klaus
Published: April 2006

1. Recently Weiss [7] constructed a stochastic model for the spread of diseases e.g. typhoid, by carriers. He assumed that a carrier is eliminated in (t, t + dt) with probability βrdt, where r is the number of carriers extant at time t and that a susceptible is infected in (t, t + dt) with probability arsdt where s is the number of susceptibles at time t. Thus only the carriers are responsible for the spread of the disease.
Non-linear time series regression
Authors: Hannan E. J.
Published: April 2006

In Jennrich (1969) the model

is considered, where x(n) is a sequence of i.i.d. (0, σ2) random variables and z(n; θ) is a continuous but possibly non-linear function of θ∈ Θ, Θ being a compact set in Rp. We shall use a second subscript when referring to a particular coordinate of θ0 so that θ0j is the jth coordinate. Jennrich establishes, under suitable conditions on z(n; θ) and x(n), the strong consistency and asymptotic normality of the least squares estimates of θ. Our main purpose here is to extend these results to the case where x(n) is generated by a stationary time series.
Characterization of a class of second-order density functions
Authors: Mehr C. B.
Published: April 2006

Distributions of some random variables have been characterized by independence of certain functions of these random variables. For example, let X and Y be two independent and identically distributed random variables having the gamma distribution. Laha showed that U = X + Y and V = X | Y are also independent random variables. Lukacs showed that U and V are independently distributed if, and only if, X and Y have the gamma distribution. Ferguson characterized the exponential distribution in terms of the independence of X – Y and min (X, Y). The best-known of these characterizations is that first proved by Kac which states that if random variables X and Y are independent, then X + Y and X – Y are independent if, and only if, X and Y are jointly Gaussian with the same variance. In this paper, Kac's hypotheses have been somewhat modified. In so doing, we obtain a larger class of distributions which we shall call class λ1. A subclass λ0 of λ1 enjoys many nice properties of the Gaussian distribution, in particular, in non-linear filtering.
A linear birth and death process under the influence of another process
Authors: Puri Prem S.
Published: April 2006

Let {X1 (t), X2 (t), t ≧ 0} be a bivariate birth and death (Markov) process taking non-negative integer values, such that the process {X2(t), t ≧ 0} may influence the growth of the process {X1(t), t ≧ 0}, while the process X2 (·) itself grows without any influence whatsoever of the first process. The process X2 (·) is taken to be a simple linear birth and death process with λ2 and µ2 as its birth and death rates respectively. The process X1 (·) is also assumed to be a linear birth and death process but with its birth and death rates depending on X2 (·) in the following manner: λ (t) = λ1 (θ + X2 (t)); µ(t) = µ1 (θ + X2 (t)). Here λ i, µi and θ are all non-negative constants. By studying the process X1 (·), first conditionally given a realization of the process {X2 (t), t ≧ 0} and then by unconditioning it later on by taking expectation over the process {X2 (t), t ≧ 0} we obtain explicit solution for G in closed form. Again, it is shown that a proper limit distribution of X1 (t) always exists as t→∞, except only when both λ1 > µ1 and λ2 > µ2. Also, certain problems concerning moments of the process, regression of X1 (t) on X2 (t); time to extinction, and the duration of the interaction between the two processes, etc., are studied in some detail.
A branching process with disasters
Authors: Kaplan Norman , Sudbury Aidan , Nilsen Trygve S.
Published: April 2006

A population process is considered where particles reproduce according to an age-dependent branching process, and are subjected to disasters which occur at the epochs of an independent renewal process. Each particle alive at the time of a disaster, survives it with probability p and the survival of any particle is assumed independent of the survival of any other particle. The asymptotic behavior of the mean of the process is determined and as a consequence, necessary and sufficient conditions are given for extinction.
The simple branching process with infinite mean. I
Authors: Seneta E.
Published: April 2006

The simple branching process {Zn} with mean number of offspring per individual infinite, is considered. Conditions under which there exists a sequence {pn} of positive constants such that pn log (1 +Zn) converges in law to a proper limit distribution are given, as is a supplementary condition necessary and sufficient for pn~ constant cn as n→∞, where 0 < c < 1 is a number characteristic of the process. Some properties of the limiting distribution function are discussed; while others (with additional results) are deferred to a sequel.
On a characterization of the exponential distribution by order statistics
Authors: Ahsanullah M.
Published: April 2006

Let X1, X2, …, Xn be a random sample of size n from a population with probability density function f(x), x >0, and let X1,n < X2,n < … < Xn,n be the associated order statistics. A characterization of the exponential distribution is shown by considering the identical distribution of the random variables nX1,n and (n − i + 1)(X1,n −; Xi–1,n) for one i and one n with 2 ≦ i ≦ n.
A theorem on compositions of random probability generating functions and applications to branching processes with random environments
Authors: Kaplan Norman
Published: April 2006

The results of this paper deal directly with the behavior of compositions of random probability generating functions. These results are then applied to the theory of branching processes with random environments. In particular, it is shown that it is not possible to strengthen many of the existing limit theorems on this subject.
Radon-Nikodym derivatives, passages and maxima for a Gaussian process with particular covariance and mean
Authors: Bar-David Israel
Published: April 2006

We find expressions for the R–N derivative of the stationary Gaussian process with the particular covariance and mean, respectively, R(t, s) = max(1 – |t – s|, 0) and m(t)= aR(t, D), 0 ≦ D ≦ 1, within the time interval [0, 1]. We use these results, and a lemma on multiple reflections of the Wiener process, to find formulae for the probabilities of first passage time and maxima in [0, 1], and bounds on the former within [– 1, 1]. While previous work dealt extensively with the zero mean process, mean functions, as defined here, appear in signal detection and parameter estimation problems under the hypothesis that a rectangular signal centered at t = D is present in an observed process.
A characterization of triangular arrays which are expectations of order statistics
Authors: Kadane Joseph B.
Published: April 2006

Necessary and sufficient conditions are found for a triangular array (finite or infinite) to be expected values of order statistics. The conditions are a wellknown recurrence relation, and a moment condition.
Gordin's theorem and the periodogram
Authors: Rootzén Holger
Published: April 2006

In 1968 M. I. Gordin proved a very strong central limit theorem for stationary, ergodic sequences by means of approximation with martingales. In the present paper Gordin's theorem is generalized to cover also the periodogram of a stationary sequence, and the restriction of ergodicity is removed. It is noted that known central limit theorems for stationary processes can often be generalized to the periodogram by means of this result.
A secretary problem with uncertain employment
Authors: Smith M. H.
Published: April 2006

A ‘Secretary Problem’ with no recall but which allows the applicant to refuse an offer of employment with a fixed probability 1 – p, (0 < p < 1), is considered. The optimal stopping rule and the maximum probability of employing the best applicant are derived.
Semi-Markovian manpower models in continuous time
Authors: Mehlmann Alexander
Published: April 2006

This paper presents the general properties of the semi-Markovian manpower model in continuous time. The asymptotic relation for the population numbers in various grades is based on the forces of transition zij(u) from state i to state j at duration u.
Another martingale bound on the waiting-time distribution in GI/G/1 queues
Authors: Tan Harry H.
Published: April 2006

A new upper bound on the stationary waiting-time distribution of a GI/G/1 queue is derived following Kingman's martingale approach. This bound is generally stronger than Kingman's upper bound and is sometimes stronger than an upper bound derived by Ross.
On multiple covering of a circle with random arcs
Authors: Holst Lars
Published: April 2006

On a circle of unit circumference arcs of length a are placed at random. Let Nα be equal to the necessary number of arcs to cover at least the length 1 − p, 0 ≦ p < 1, of the circumference at least m (≧1) times. In the present paper limit distributions of Nα are derived when α → 0. Some results for spacings are also obtained.
On the continuity and the positivity of the finite part of the limit distribution of an irregular branching process with infinite mean
Authors: Cohn H. , Schuh H.-J.
Published: April 2006

It is shown that the limiting random variable W(si) of an irregular branching process with infinite mean, defined in [5], has a continuous and positive distribution on {0 < W(si) < ∞}. This implies that for all branching processes (Zn) with infinite mean there exists a function U such that the distribution of V = limnU(Zn)e–n a.s. is continuous, positive and finite on the set of non-extinction. A kind of law of large numbers for sequences of independent copies of W(si) is derived.
Mean duration time for a general epidemic process
Authors: Gladstien Billard
Published: April 2006

A general epidemic process is said to be completed whenever the number of susceptibles or the number of infectives reduces to zero. The mean duration time for this process to be completed is derived.
The mixed exponential solution to the first-order autoregressive model
Authors: Lawrance A. J.
Published: April 2006

This paper gives the distribution of the independent variable in a first-order autoregressive equation which is necessary for the modelled variable to have a mixed exponential marginal distribution. Restricting attention first to a mixture of two exponentials which is probabilistic, a solution is shown to exist over a restricted range of the first serial correlation; tabulations of the boundary values are given. The independent variable has a distribution which includes a discrete component at zero and a not necessarily probabilistic mixture of three exponentials. The marginal distribution is then considered with a negative mixture weight; this weight is shown to be lower bounded in value, but not to depend on the first serial correlation.
On random simplices in product distributions
Authors: Maehara Hiroshi
Published: April 2006

It is proved that the r-dimensional volume Vn of the r-simplex spanned by r + 1 sample points taken from the n-fold product distribution of a distribution F is asymptotically normal as n →∞.
Conditions for evolutionarily stable strategies
Authors: Abakuks Andris
Published: April 2006

It is pointed out that the conditions given by Haigh (1975) for finding evolutionarily stable strategies corresponding to a given matrix are sufficient, but not always necessary. An example is given, and an amended version of the necessary and sufficient conditions is stated.
Repeated matrix games
Authors: Kamerud Dana B.
Published: April 2006

A matrix game is played repeatedly, with the actions taken at each stage determining both a reward paid to Player I and the probability of continuing to the next stage. An infinite history of play determines a sequence (Rn) of such rewards, to which we assign the payoff lim supn (R1 + · ·· + Rn). Using the concept of playable strategies, we slightly generalize the definition of the value of a game. Then we find sufficient conditions for the existence of a value and for the existence of stationary optimal strategies (Theorems 8 and 9). An example shows that the game need not have a value (Example 4).
Extinction probability, regularity and asymptotic growth of Markovian populations
Authors: Lenz Norbert
Published: April 2006

The distribution of the maximum and the extinction probability for a Markovian population is derived. Asymptotic growth is described, using the sequence of sojourn times. A regularity criterion for the processes under consideration exists under certain assumptions. For a class of processes with specific population-dependent transition rates the asymptotic behaviour is given explicitly.
On the size distribution for some epidemic models
Authors: Watson Ray
Published: April 2006

We consider the standard epidemic model and several extensions of this model, including Downton's carrier-borne epidemic model. A random time-scale transformation is used to obtain equations for the size distribution and to derive asymptotic approximations for the size distribution for each of the models
Martingale convergence in the branching random walk
Authors: Biggins J. D.
Published: April 2006

A result like the Kesten-Stigum theorem is obtained for certain martingales associated with the branching random walk. A special case, when a ‘Malthusian parameter’ exists, is considered in greater detail and a link with some known results about the Crump-Mode model for a population is established.
Diffusion approximations for the cooperative service of voice and data messages
Authors: Lehoczky J. P. , Gaver D. P.
Published: April 2006

A diffusion approximation is developed for a voice and data communication system. Voice traffic operates as an M/M/v/v loss system, while data is a Markovian queueing system with a random number of channels assigned. The data process is shown to be approximated by a certain Wiener process with reflecting barrier at 0. System behavior is described using this approximation. The methodology is based on the work of Burman (1979).
Asymptotic inference for an Ising lattice III. Non-zero field and ferromagnetic states
Authors: Pickard David K.
Published: April 2006

In previous papers (1976), (1977) limit theorems were obtained for the classical Ising model in the absence of an external magnetic field, thereby providing a basis for asymptotic inference. The present paper extends these results to arbitrary external magnetic fields. Statistical inference for this model is important because its nearest-neighbour interactions provide a natural first approximation to spatial interaction among binary variables located on square lattices.

The most interesting behaviour occurs in zero field and at or beyond the critical point. In this case, the central limit result for nearest-neighbour interactions requires an unusual norming, the limiting variances may depend on the nature of the boundary conditions, and there cannot be any central limit result for external magnetic field. The implications of these phenomena for statistical inference are also discussed. In particular, the maximum likelihood estimator of magnetic field is not consistent. Rather it appears to have a non-trivial asymptotic distribution.
On the optimal assignment of customers to parallel servers
Authors: Weber Richard R.
Published: April 2006

We consider a queuing system with several identical servers, each with its own queue. Identical customers arrive according to some stochastic process and as each customer arrives it must be assigned to some server's queue. No jockeying amongst the queues is allowed. We are interested in assigning the arriving customers so as to maximize the number of customers which complete their service by a certain time. If each customer's service time is a random variable with a non-decreasing hazard rate then the strategy which does this is one which assigns each arrival to the shortest queue.
A note on simultaneous recurrence conditions on a set of denumerable stochastic matrices
Authors: Federgruen A. , Hordijk A. , Tijms H. C.
Published: April 2006

In this paper we consider a set of denumerable stochastic matrices where the parameter set is a compact metric space. We give a number of simultaneous recurrence conditions on the stochastic matrices and establish equivalences between these conditions. The results obtained generalize corresponding results in Markov chain theory to a considerable extent and have applications in stochastic control problems.
Chernoff's theorem in the branching random walk
Authors: Biggins J. D.
Published: April 2006

If Fn∗ is the n-fold Stieltjes convolution of the increasing function F, then a version of Chernoff's theorem, on the limiting behaviour of (Fn∗(na))1/n, is established for Fn∗. If Z(n)(t) is the number of the nth-generation people to the left of t in a supercritical branching random walk then an analogous result is proved for Z(n).
The volume of a random simplex in an n-ball is asymptotically normal
Authors: Ruben Harold
Published: April 2006

A proof is given of a conjecture in the literature of geometrical probability that the r-content of the r-simplex whose r + 1 vertices are independent random points of which p are uniform in the interior and q uniform on the boundary of a unit n-ball (1 ≦ r ≦ n; 0 ≦ p, q ≦ r + 1, p + q = r + 1) is asymptotically normal (n →∞) with asymptotic mean and variance and , respectively.
Limit theorems for out guesses with mean-guided second guessing
Authors: Hwang Jiunn Tzon , Zidek James V.
Published: April 2006

A second guesser, G2, proposes to guess ‘smaller' or ‘larger' on each of n contests, i, according as , or where Xi, i = 1, ···, n are the revealed guesses of the first guesser, G1. G2 wins contest i if his assertion about the size of the target quantity θi, is more accurate than that of G1, Xi, i = 1, ···, n. Otherwise G 1 is the winner. Laws of large numbers are derived for G2's win totals for arbitrary configurations of θi. Limiting distributions are obtained for the first guesser's win totals in two special cases, the first where the θi are highly concentrated and the second where they are widely dispersed. G2 enjoys an enormous advantage over G1 in the former case, as intuition would suggest.
Covering the circle with random arcs of random sizes
Authors: Siegel Andrew F. , Holst Lars
Published: April 2006

Consider the random uniform placement of a finite number of arcs on the circle, where the arc lengths are sampled from a distribution on (0, 1). We provide exact formulae for the probability that the circle is completely covered and for the distribution of the number of uncovered gaps, extending Stevens's (1939) formulae for the case of fixed equal arc lengths. A special class of arc length distributions is considered, and exact probabilities of coverage are tabulated for the uniform distribution on (0, 1). Some asymptotic results for the number of gaps are also given.
Random coverage of the circle and asymptotic distributions
Authors: Hüsler J.
Published: April 2006

Place n arcs of equal length an uniformly at random on the circumference of a circle. We discuss the limiting distributions of the number of gaps, the length of the maximum gap and the uncovered proportion of the circle, depending on the asymptotic behaviour of an → 0.
The secretary problem with an unknown number of candidates
Authors: Abdel-hamid A. R. , Bather J. A. , Trustrum G. B.
Published: April 2006

When the number of candidates is unknown, the problem of selecting the best during a sequence of interviews has many reasonable solutions. A simple condition for admissibility is established and it is shown that the class of Bayes solutions obtained by treating the number of candidates as a random variable is by no means complete. On the other hand, there is a single improper prior distribution for which the extended Bayes solutions constitute the whole family of admissible procedures.
Strong ergodicity for continuous-time, non-homogeneous Markov chains
Authors: Scott Mark , Arnold Barry C. , Isaacson Dean L.
Published: April 2006

Characterizations of strong ergodicity for Markov chains using mean visit times have been found by several authors (Huang and Isaacson (1977), Isaacson and Arnold (1978)). In this paper a characterization of uniform strong ergodicity for a continuous-time non-homogeneous Markov chain is given. This extends the characterization, using mean visit times, that was given by Isaacson and Arnold.
Critical phenomena in semi-infinite systems
Authors: Hammersley J. M.
Published: April 2006

This paper discusses the asymptotic behaviour, and in particular the critical singularities, of the generating functions for Pólya walks with a given fraction of visits to a hyperplane when the walk is or is not constrained to be on one side of that hyperplane. The three-dimensional case has applications in physics and chemistry.
Entropy and martingales in Markov chain models
Authors: Seneta E.
Published: April 2006

The concept of entropy in models is discussed with particular reference to the work of P.A.P. Moran. For a vector-valued Markov chain {Xk} whose states are relative-frequency (proportion) tables corresponding to a physical mixing model of a number N of particles over n urns, the definition of entropy may be based on the usual information-theoretic concept applied to the probability distribution given by the expectation . The model is used for a brief probabilistic assessment of the relationship between Boltzmann's Η-Theorem, the Ehrenfest urn model, and Poincaré's considerations on the mixing of liquids and card shuffling, centred on the property of an ultimately uniform distribution of a single particle. It is then generalized to the situation where the total number of particles fluctuates over time, and martingale results are used to establish convergence for .
The convexity of the mean queue size of the M/M/c queue with respect to the traffic intensity
Authors: Grassmann W.
Published: April 2006

In this paper, we show that the expected number in an M/M/c queue is convex with respect to the traffic intensity. The proof is conducted by expressing the second derivative of the expected queue size as the sum of non-negative terms.
First-passage time of Markov processes to moving barriers
Authors: Tuckwell Henry C. , Wan Frederic Y. M.
Published: April 2006

The first-passage time of a Markov process to a moving barrier is considered as a first-exit time for a vector whose components include the process and the barrier. Thus when the barrier is itself a solution of a differential equation, the theory of first-exit times for multidimensional processes may be used to obtain differential equations for the moments and density of the first-passage time of the process to the barrier. The procedure is first illustrated for first-passage-time problems where the solutions are known. The mean first-passage time of an Ornstein–Uhlenbeck process to an exponentially decaying barrier is then found by numerical solution of a partial differential equation. Extensions of the method to problems involving Markov processes with discontinuous sample paths and to cases where the process is confined between two moving barriers are also discussed.
The kin number problem in a multitype Galton–Watson population
Authors: Joffe A. , Waugh W. A. O'n.
Published: April 2006

The kin number problem in its simplest form is that of the relationship between sibship sizes and offspring numbers. The fact that the distributions are different, and the relationship between the two, is well known to demographers. It is important in such applications as estimating fertility from sibship rather than offspring counts. Further studies have been made, concerning relatives of other degrees of affinity than siblings, but these did not usually yield joint distributions. Recently this aspect of the problem has been studied in the framework of a Galton–Watson process (Waugh (1981), Joffe and Waugh (1982)).

In these studies the population is treated as monotype. Applications such as pedigree studies of diseases require a multitype approach (in the example, two types: victims and others). In this paper such a study is undertaken. The existence of more than one type complicates the time-reversal used in the previous studies, and raises questions about the way in which the focal individual (called ‘Ego') is sampled. These are dealt with, and joint distributions obtained, under a number of sampling schemes which might arise naturally.
The proportion of the population never hearing a rumour
Authors: Sudbury Aidan
Published: April 2006

For a model of a rumour, first given a non-rigorous treatment by Maki and Thompson, it is shown that the proportion of the population never hearing the rumour converges in probability to 0.203 as the population size tends to∞.
An asymptotic formula for the distribution of the maximum of a Gaussian process with stationary increments
Authors: Berman Simeon M.
Published: April 2006

Let X(t), t≧0, be a Gaussian process with mean 0 and stationary increments. If the incremental variance function σ2(t) is convex and σ2(t) = o(t) for t → 0, then P(max[o,t]X(s) > u) ~ P(X(t) > u) for u → ∞ and each t > 0.
Recurrence formula and the maximum likelihood estimation of the age in a simple branching process
Authors: Adès M. , Dion J.-P. , Labelle G. , Nanthi K.
Published: April 2006

In this paper, we consider a Bienaymé– Galton–Watson process {Xn; n ≧ 0; Xn = 1} and develop a recurrence formula for P(Xn = k), k = 1, 2, ···. The problem of obtaining the maximum likelihood estimate of the age of the process when p0 = 0 is discussed. Furthermore the maximum likelihood estimate of the age of the process when the offspring distribution is negative binomial (p0 ≠ 0) is obtained, and a comparison with Stigler's estimator (1970) of the age of the process is made.
Asymptotic behavior of Markov systems
Authors: Vassiliou P.-C. G.
Published: April 2006

In this paper we study the asymptotic behavior of Markov systems and especially non-homogeneous Markov systems. It is found that the limiting structure and the relative limiting structure exist under certain conditions. The problem of weak ergodicity in the above non-homogeneous systems is studied. Necessary and sufficient conditions are provided for weak ergodicity. Finally, we discuss the application of the present results in manpower systems.
New bounds for the thermal energy storage process with stationary input
Authors: Haslett J.
Published: April 2006

The process {Xn}, defined by Xn+ 1 = max{Yn+ 1 + αßXn, ßXn}, with αand ß in [0, 1) and {Yn} stationary, arises in studies of solar thermal energy systems. Bounds for the stationary mean EX are given, which are more general and in some cases tighter, than those previously available.
Compartmental models with transfer delays: a semi-Markov approach
Authors: Leitnaker Mary G. , Purdue Peter
Published: April 2006

Compartmental models for which transfer from one compartment to another takes a non-negligible time have been studied in the deterministic case. These models rely on the use of differential equations with delayed arguments. In this paper we show how the well-known structure of the semi-Markov process can be used to analyse stochastic compartmental models with transfer delays. Evaluation of the limiting behavior is much simpler in the stochastic model than in previous deterministic formulations. In addition, time-dependent behavior can be analysed using numerical quadrature methods.
Optimal design of a storage system with constant or linear release rate
Authors: De Morais Paulo Renato
Published: April 2006

This paper is concerned with the determination of the optimal release rate for a continuous storage system. The input to the store is assumed to be a compound Poisson process (with non-negative jumps), and its content is released either at a constant rate or at a linear rate. Rewards are collected at an output-dependent rate and are continuously discounted at a constant rate. The problem consists in finding the optimal release rate which maximizes the infinite-horizon expected discounted return. This problem is solved by deriving an explicit solution for the expected discounted return, from which the optimal release rate can be found.
First-passage-time moments of Markov processes
Authors: Yao David D.
Published: April 2006

We consider the first-passage times of continuous-time Markov chains. Based on the approach of generalized inverse, moments of all orders are derived and expressed in simple, explicit forms in terms of the ‘fundamental matrix'. The formulas are new and are also efficient for computation.
A first-passage problem for a two-dimensional controlled random walk
Authors: Lalley S.
Published: April 2006

The process of interest is a controlled random walk in two dimensions: whenever the walker is above the main diagonal, the next increment to his position is chosen from a distribution FA; whenever the walker is below the diagonal, the next increment comes from another distribution FB. The two distributions have mean vectors which tend to push the walker back toward the diagonal. We analyze the problem of first passage to the first quadrant, obtaining explicit representations for the limiting first-entry distribution and expected first-passage time.
A search game with one object and two searchers
Authors: Nakai Teruhisa
Published: April 2006

We consider a non-zero-sum game in which two searchers (player I and II) compete with each other for quicker detection of an object hidden in one of n boxes. Let p (q) be the prior location distribution of the object for player I (II). Exponential detection functions are assumed for both players. Each player wishes to maximize the probability that he detects the object before the opponent detects it. In the general case, a Nash equilibrium point is obtained in the form of a solution of simultaneous differential equations. In the case of p = q, we obtain an explicit solution showing the surprising result that both players have the same equilibrium strategy even though the detection rates are different.
A correlated queue with infinitely many servers
Authors: Langaris C.
Published: April 2006

This work analyses a queueing mechanism with infinitely many servers in which the interarrival interval T preceding the arrival of a customer and his service time S are assumed correlated. A bivariate distribution with negative exponential marginals is used and the Laplace transforms pn (z) of the system probabilities in transient state are obtained. Closed-form expressions for the steady-state probabilities pn and their moments are given too. Finally the output process is investigated and conclusions are drawn from numerical calculations.
On limiting laws for the convex hull of a sample
Authors: Brozius Henk , De Haan Laurens
Published: April 2006

The limiting behaviour of the convex hull of a sample in is studied using the support function. Results like that of Eddy and Gale (1981) are proved without the condition of spherical symmetry from that paper.
The control of a finite dam with penalty cost function: Markov input rate
Authors: Attia F. A.
Published: April 2006

The long-run average cost per unit time of operating a finite dam controlled by a policy (Lam Yeh (1985)) is determined when the cumulative input process is the integral of a Markov chain. A penalty cost which accrues continuously at a rate g(X(t)), where g is a bounded measurable function of the content, is also introduced. An example where the input rate is a two-state Markov chain is considered in detail to illustrate the computations.
On sojourn time in Jackson networks of queues
Authors: Lemoine Austin J.
Published: April 2006

This paper is about representations for equilibrium sojourn time distributions in Jackson networks of queues. For a network with N single-server nodes let hi be the Laplace transform of the residual system sojourn time for a customer ‘arriving' to node i, ‘arrival' meaning external input or internal transfer. The transforms {hi : i = 1, ···, N} are shown to satisfy a system of equations we call the network flow equations. These equations lead to a general recursive representation for the higher moments of the sojourn time variables {Ti : i = 1, ···, N}. This recursion is discussed and then, by way of illustration, applied to the single-server Markovian queue with feedback.
Tight bounds on the sensitivity of generalised semi-Markov processes with a single generally distributed lifetime
Authors: Coyle A. J. , Taylor P. G.
Published: April 2006

There are some generalised semi-Markov processes (GSMP) which are insensitive, that is the value of some performance measures for the system depend only on the mean value of lifetimes and not on their actual distribution. In most cases this is not true and a performance measure can take on a number of values depending on the lifetime distributions. In this paper we present a method for finding tight bounds on the sensitivity of performance measures for the class of GSMPs with a single generally distributed lifetime. Using this method we can find upper and lower bounds for the value of a function of the stationary distribution as the distribution of the general lifetime ranges over a set of distributions with fixed mean. The method is applied to find bounds on the average queue length of the Engset queue and the time congestion in the GI/M/n/n queueing system.
A simple increasing process
Authors: Syski Ryszard
Published: April 2006

An example of a simple integrable increasing process, possessing special properties relative to different filtrations, is examined from the point of view of probabilistic potential theory.
Convergence rates for M/G/1 queues and ruin problems with heavy tails
Authors: Asmussen Søren , Teugels Jozef L.
Published: April 2006

The time-dependent virtual waiting time in a M/G/1 queue converges to a proper limit when the traffic intensity is less than one. In this paper we give precise rates on the speed of this convergence when the service time distribution has a heavy regularly varying tail.

The result also applies to the classical ruin problem. We obtain the exact rate of convergence for the ruin probability after time t for the case where claims arrive according to a Poisson process and claim sizes are heavy tailed.

Our result supplements similar theorems on exponential convergence rates for relaxation times in queueing theory and ruin probabilities in risk theory.
A product-form ‘loss network' with a form of queueing
Authors: Berezner S. A. , Krzesinski A. E. , Taylor P. G.
Published: April 2006

We show that a form of queueing can be introduced into the standard fixed-routing loss network model while retaining a product-form invariant measure.
Comparing sums of exchangeable Bernoulli random variables
Authors: Lefèvre Claude , Utev Sergey
Published: April 2006

The paper is first concerned with a comparison of the partial sums associated with two sequences of n exchangeable Bernoulli random variables. It then considers a situation where such partial sums are obtained through an iterative procedure of branching type stopped at the first-passage time in a linearly decreasing upper barrier. These comparison results are illustrated with applications to certain urn models, sampling schemes and epidemic processes. A key tool is a non-standard hierarchical class of stochastic orderings between discrete random variables valued in {0, 1,· ··, n}.
On the inverse of the first hitting time problem for bidimensional processes
Authors: Lefebvre Mario
Published: April 2006

Bidimensional processes defined by dx(t) = ρ (x, y)dt and dy(t) = m(x, y)dt + [2v(x, y)]1/2dW(t),

where W(t) is a Wiener process, are considered. Let T(x, y) be the first time the process (x(t), y(t)), starting from (x, y), hits the boundary of a given region in . A theorem is proved that gives necessary and sufficient conditions for a given complex function to be considered as the moment generating function of T(x, y) for some bidimensional diffusion process. Examples are given where the theorem is used to construct explicit solutions to first hitting time problems and to compute the infinitesimal moments that correspond to the chosen moment generating function.