bluuebunny/crossref_metadata_2025 huggingface dataset:
Plant systematics in the next 50 years—re‐mapping the new frontier
Authors: Sytsma Kenneth J. , Pires J. Chris
Published: April 2006

Sytsma, K. J. & Pires, J. C.: Plant systematics in the next 50 years—re‐mapping the new frontier. ‐ Taxon 50: 713–732. 2001. ‐ ISSN 0040‐0262.

In the historical context of plant systematics over the last 50 years, systematics is examined in terms of where it is now, where it is headed, where it should be, and how it should get there. Issues and concerns of the past decades are still with us today. Molecular systematics has become the over‐arching field in systematics, but each of eight other areas (genome, chromosomes, morphology and anatomy, development, population biology, speciation, floristics and monography, nomenclature and classification) are evaluated. A revolution in systematics is not necessary for the next 50 years in plant systematics. What is needed is a re‐mapping of our discipline that involves four elements for the future growth and health of botanical systematics: plant systematics and its utility, dialogue with other disciplines, multi‐disciplinary training, and a pluralistic viewpoint.
Phylogenetic relationships in Anthemis L. (Compositae, Anthemideae) based on nrDNA ITS sequence variation
Authors: Oberprieler Christoph
Published: April 2006

Oberprieler, C.: Phylogenetic relationships in Anthemis L. (Compositae, Anthemideae) based on nrDNA ITS sequence variation. Taxon 50: 745–762. 2001. ISSN 0040‐0262.

Sequences of the nrDNA internal transcribed spacer (ITS) region were analysed for 29 representatives of Anthemis L. and six outgroup taxa of Anthemideae (Compositae) to study the delimitation and the infrageneric taxonomy of this large and widespread Eurasian and African genus. Species of Anthemis included all subgenera and sections traditionally used in supraspecific classifications of the genus. Maximum parsimony (MP), maximum likelihood (ML), and distance (neighbor joining, NJ) analyses were carried out for phylogenetic reconstructions. The results suggest that the genus, in its traditional circumscription, is not monophyletic due to the consistent placement of a member of Tripleurospermum amidst the Anthemis representatives. Subdivision of Anthemis into two subgenera (A. subg. Anthemis, A. subg. Cota) is supported, with the exception of the placement of A. sect. Chiae and sect. Odontostephanae which fall outside A. subg. Anthemis. Within A. subg. Anthemis, life form dependent delimitation of A. sect. Anthemis (annuals) against A. sect. Hiorthia (perennials) is not supported, whereas the monophyly of other sections (A. sect. Maruta, A. sect. Rascheyanae) is confirmed including the placement of Ammanthus Boiss. & Heldr. into Anthemis subg. Anthemis.
Phylogenetic relationships in Polygalaceae based on plastid DNA sequences from the trnL‐F region
Authors: Persson Claes
Published: April 2006

Persson, C.: Phylogenetic relationships in Polygalaceae based on plastid DNA sequences from the trnL‐F region. ‐ Taxon 50: 763–779. 2001. ‐ ISSN 0040‐0262.

Seventy‐three plastid DNA sequences from the trnL‐F region were used to infer phylogenetic relationships among Polygalaceae. The analysis indicates that Xanthophyllum is the sister group to the remainder of genera in Polygalaceae. Monophyly of tribes Polygaleae and Carpolobieae is corroborated, whereas monophyly of Moutabeae could not be confirmed. Although intergeneric relationships within Polygaleae are poorly resolved, most traditional genera are corroborated as monophyletic. However, Polygala and Bredemeyera s.l. form two exceptions and are grossly polyphyletic. Acanthocladus and Badiera (incl. Hebecarpa), taxa often assigned to Polygala, are more closely related to Bredemeyera s.str. than to other Polygala. Likewise, Bredemeyera s.l. is broadly polyphyletic since Comesperma and Bredemeyera colletioides (sect. Hualania) have their closest relatives among other genera. Furthermore, Hualania is also polyphyletic since Bredemeyera microphylla appears as the sister to the Hebecarpa‐Badiera clade. Unlike a previous morphological analysis, Monnina is strongly supported as monophyletic by trnL‐F data, but internal relationships are partly unresolved. Species of Polygala sensu Chodat have a tendency to group by geographical distribution rather than after traditional sectional affiliation. Thus, although resolution is poor, it is suspected that several sections of Polygala are not monophyletic and need to be recircumscribed.
Family name listings modified in Appendix IIB of the Saint Louis Code
Authors: Turland Nicholas J. , Barrie Fred R.
Published: April 2006

Turland, N. J. & Barrie, F. R. 2001. Family name listings modified in Appendix IIB of the Saint Louis Code. ‐ Taxon 50: 897–903. 2001. ‐ ISSN 0040‐0262.

The Nomenclature Section of the XVI International Botanical Congress authorised the revision of Appendix IIB of the International Code of Botanical Nomenclature. We provide a list of the entries which have been modified editorially in the Saint Louis Code.
The present status of the names applicable to species and infraspecific taxa of Erioderma (lichenised ascomycetes) included in Zahlbruckner's Catalogus
Authors: Jørgensen Per M.
Published: April 2006

Jørgensen, P. M.: The present status of the names applicable to species and infraspecific taxa of Erioderma (lichenised ascomycetes) included in Zahlbruckner's Catalogus. – Taxon 50: 525–542. 2001. – ISSN 0040‐0262.

All 26 names of species and infraspecific taxa included in Zahlbruckner's Catalogus and applicable to Erioderma are listed and typified with comments on their taxonomy and distribution. The author recognises only 10 of the 17 species accepted by Zahlbruckner, but also indicates the existence of more than 10 undescribed species, mainly in South America. One new combination E. leylandii subsp. velligerum (Tuck.) P.M. Jørg. (= E. chilense Mont.) is made.
Taxonomic study of Taiwan Astragalus based on genetic variation
Authors: Luo Miaw‐Chyi , Hwu Kae‐Kang , Huang Tseng‐Chieng
Published: April 2006

Luo, Miaw‐Chyi, Hwu, Kae‐Kang & Huang, Tseng‐Chieng: Taxonomic study of Taiwan Astragalus based on genetic variation. – Taxon 49: 35‐46. 2000. – ISSN 0040‐0262.

Three species of Astragalus, A. sinicus L., A. nokoensis Sasaki, and A. nankotaizanensis Sasaki, occur in Taiwan, and the latter two are endemic. Randomly amplified polymorphic DNA (RAPD) analysis was used to determine genetic variation of the three species. Bands in RAPD profiles were treated as independent loci. From studies of 207 individuals in eight populations of Astragalus, a total of 131 RAPD bands was generated using eleven 10‐mer primers. Genetic similarity among 207 individuals in the eight populations was calculated using Jaccard's coefficient. The results of the UPGMA cluster analysis were in broad agreement with previous classifications of these three species, which clearly discriminated between Astragalus sinicus, A. nankotaizanensis, and A. nokoensis. Based on RAPD data, A. nankotaizanensis and A. nokoensis were slightly closer than A. nokoensis and A. sinicus. A positive relationship between genetic distance and geographical distance for populations of A. nokoensis was also seen. The results of this study do not support classification of these three species into one species as A. sinicus s.l.
Identity and typification of Corallorhiza punctata and C. bulbosa (Orchidaceae)
Authors: Salazar Gerardo A. , Freudenstein John V.
Published: April 2006

Salazar, G. A. & Freudenstein, J. V.: Identity and typification of Corallorhiza punctata and C. bulbosa (Orchidaceae). ‐ Taxon 47: 51–54. 1998. ‐ ISSN 0040‐0262.

The identity of two orchid taxa described from Mexico as Corallorhiza punctata and C. bulbosa is discussed in the light of original material located at W, and not at P as would be expected. It is concluded that C. punctata falls within the older C. wisteriana and should be treated as a synonym, whereas, C. bulbosa deserves specific recognition, being distinguished from the similar C. maculata by the much smaller mentum which is non‐decurrent on the ovary, and the numerous, minute spots on the lip.
Cynanchum – Rhodostegiella – Vincetoxicum – Tylophora (Asclepiadaceae): new considerations on an old problem
Authors: Liede Sigrid
Published: April 2006

Liede, S.: Cynanchum – Rhodostegiella – Vincetoxicum – Tylophora (Asclepiadaceae): new considerations on an old problem. – Taxon 45: 193‐211. 1996. – ISSN 0040‐0262.

On the basis of morphological and chemical data, the genus Vincetoxicum is recognized as separate from Cynanchum. Tylophora is identified as the closest relative of Vincetoxicum. In consequence, eleven new combinations in Vincetoxicum are proposed. The C. auriculatum group is recognized as C. sect. Rhodostegiella. Tylophoropsis must be included in Tylophora, which results in one new combination.
Mankyua (Ophioglossaceae): a new fern genus from Cheju Island, Korea
Authors: Sun Byung‐Yun , Kim Moon Hong , Kim Chul Hwan , Park Chong‐Wook
Published: April 2006

Sun, B.‐Y., Kim, M. H., Kim, C. H. & Park, C.‐W.: Mankyua (Ophioglossaceae): a new fern genus from Cheju Island, Korea. ‐ Taxon 50: 1019–1024. 2001. ‐ ISSN 0040–0262.

Mankyua chejuense gen. & sp. nov. (Ophioglossaceae) is described from a lowland swampy area of Cheju Island off the south coast of the Korean Peninsula. The diagnostic characters include: (1) ternately divided compound trophophore; (2) linear and fleshy sporophore branched at base; and (3) creeping rhizome with proliferous roots. The new fern is somewhat morphologically related to Helminthostachys and Ophioglossum, but distinct enough to merit generic status.
Reinstatement of the name Richterago Kuntze and recircumscription of the genus to include species formerly treated as Actinoseris (Endl.) Cabrera (Compositae, Mutisieae)
Authors: Roque Nádia , Pirani José Rubens
Published: April 2006

Roque, N. & Pirani, J. R.: Reinstatement of the name Richterago Kuntze and recircumscription of the genus to include species formerly treated as Actinoseris (Endl.) Cabrera (Compositae, Mutisieae). – Taxon 50: 1155–1160. 2001. – ISSN 0040–0262.

Morphological studies of Actinoseris (Endl.) Cabrera and Gochnatia Kunth indicate that the species currently included in Gochnatia sect. Discoseris Cabrera should be transferred to Actinoseris. With this new circumscription, Richterago Kuntze is the correct generic name, having priority over Actinoseris. This paper presents a morphological description of Richterago and a nomenclatural treatment with seven new combinations.
The busy period of the Ek/G/1 queue by finite waiting room
Authors: Truslove A. L.
Published: April 2006

For the Ek/G/1 queue with finite waiting room the phase technique is used to analyse the Markov chain imbedded in the queueing process at successive instants at which customers complete service, and the distribution of the busy period, together with the number of customers who arrive, and the number of customers served, during that period, is obtained. The limit as the size of the waiting room becomes infinite is found.
Extreme values and crossings for theX2-Process and Other Functions of Multidimensional Gaussian Processes, by Reliability Applications
Authors: Lindgren Georg
Published: April 2006

Extreme values of non-linear functions of multivariate Gaussian processes are of considerable interest in engineering sciences dealing with the safety of structures. One then seeks thesurvivalprobability

whereX(t) = (X1(t), …,Xn(t)) is a stationary, multivariate Gaussianloadprocess, andSis asafe region.In general, the asymptotic survival probability for largeT-values is the most interesting quantity.

By considering the point process formed by the extreme points of the vector processX(t), and proving a general Poisson convergence theorem, we obtain the asymptotic survival probability for a large class of safe regions, including those defined by the level curves of any second- (or higher-) degree polynomial in (x1, …,xn). This makes it possible to give an asymptotic theory for the so-called Hasofer-Lind reliability index, β = inf>x∉S||x||, i.e. the smallest distance from the origin to an unsafe point.
Taxonomic monographs in relation to global Red Lists
Authors: Kirschner Jan , Kaplan Ždenek
Published: April 2006

Upon comparison with recent monographs of Juncaceae and Potamogetonaceae, the 1997 IUCN Red List of Threatened Plants is shown to be an inadequate information source for conservation decisions. A substantial proportion of names listed in the IUCN RL represent synonyms, often belonging to widespread taxa, or remain doubtful taxonomically. If a new Red List is derived from the two new monographic accounts, and compared with the 1997 IUCN RL, the correct data from the latter represent 10–25% of the former. It may concluded that the overall accuracy of the IUCN list is rather low. The importance of global taxonomic monographs as a source of basic data for the accurate compilation of Red Lists is stressed.
Weak convergence of first passage time processes
Authors: Whitt Ward
Published: April 2006

Let D = D[0, ∞) be the space of all real-valued right-continuous functions on [0, ∞) with limits from the left. For any stochastic process X in D, let the associated supremum process be S(X), wherefor any x ∊ D. It is easy to verify that S: D → D is continuous in any of Skorohod's (1956) topologies extended from D[0,1] to D[0, ∞) (cf. Stone (1963) and Whitt (1970a, c)). Hence, weak convergence Xn ⇒ X in D implies weak convergence S(Xn) ⇒ S(X) in D by virtue of the continuous mapping theorem (cf. Theorem 5.1 of Billingsley (1968)).
The identifiability of mixtures of distributions
Authors: Tallis G. M.
Published: April 2006

This paper considers aspects of the following problem. Let F(x, θ) be a distribution function, d.f., in x for all θ and a Borel measurable function of θ. Define the mixture (Robbins (1948)),

where Φ is a d.f., then it is of interest to determine conditions under which F(x) and F(x, θ) uniquely determine Φ. If there is only one Φ satisfying (1), F is said to be an identifiable mixture. Usually a consistency assumption is used whereby it is presumed that there exists at least one solution to (1).
Bounds for moment generating functions and for extinction probabilities
Authors: Brook D.
Published: April 2006

Suppose that we have a non-negative, real valued random variable x, whose distribution is governed by some unknown moment generating function M(t). Suppose further that we are given certain moments of x, then the question to be discussed in this paper is : can we find a sharp upper bounding function for the m.g.f.? It will be shown that this is usually possible both in the single variate case and in its natural extension to the multivariate case.
A stochastic calculus and its application to some fundamental theorems of natural selection
Authors: Mode Charles J.
Published: April 2006

In this paper a stochastic calculus, based on limits in quadratic mean and in probability, is introduced and applied to some fundamental theorems of natural selection. The paper is divided into five principal sections. In Section 2 some elements of stochastic calculus are given, and in Section 3 the stochastic calculus is applied to the haploid case. Section 4 is devoted to the development of an analysis of variance structure applicable to a haploid population, and in Section 5 the results of Sections 3 and 4 are generalized to cover the diploid case. Finally, Section 6 is devoted to two specific examples in which the results of previous sections apply.
Asymptotic absorption probabilities for a Poisson process
Authors: Gallot S.
Published: April 2006

An expression is found (Theorem 1) for the probability that a sample function of a Poisson process never exceeds some given function and some examples are given.
A note on a functional equation arising in Galton-Watson branching processes
Authors: Athreya Krishna B.
Published: April 2006

The functional equation ϕ(mu) = h(ϕ(u)) where is a probability generating function with 1 < m = h'(1 –) < ∞ and where F(t) is a non-decreasing right continuous function with F(0 –) = 0, F(0 +) < 1 and F(+ ∞) = 1 arises in a Galton-Watson process in a natural way. We prove here that for any if and only if This unifies several results in the literature on the supercritical Galton-Watson process. We generalize this to an age dependent branching process case as well.
Some models for interaction of renewal processes related to neuron firing
Authors: Coleman R. , Gastwirth J. L.
Published: April 2006

One area of science in which probabilistic models are beginning to play a role is in neuron firing. The firing process may be thought of in terms of electrical potentials: there is a potential difference across the membrane surrounding a neuron; this potential difference is determined by the concentrations of sodium, potassium, and chlorine ions on the two sides of the membrane. When electrical impulses arrive along the many input fibers, the potential difference changes; when it crosses a certain threshold, the neuron “fires”, that is, an impulse is discharged along the axon. Arriving impulses are of two types, those which raise and those which lower the potential inside the neuron; these are called stimuli and inhibitors, respectively. The mechanism by which stimuli and inhibitors interact in changing the neuron potential is not well understood; however, it appears that some of the stimuli cause the neuron to respond, or fire, and the inhibitors play a role in preventing the other stimuli from causing a response. The ability of stimuli to cause responses is further weakened by the decay, in the absence of arriving impulses, of the transmembrane potential toward a “resting level”, the level to which the potential is reset after a firing. While several models for the firing process have been proposed ([3], [4], [5], [6], [7], [11]), the present paper is devoted to introducing some modifications into a model proposed by Ten Hoopen and Reuver ([9], [10]). In particular, we place a time limit on the ability of inhibitors to prevent a stimulus from producing a response. Hopefully, these modifications bring their model closer to physiological reality.
Sur un theoreme de Lewis et la decomposition en facteurs premiers de la loi rectangulaire
Authors: Tortrat A.
Published: April 2006

Un théorème de Lewis [3] montre que les seuls facteurs indécomposables de la mesure de Lebesgue m sur S = [–π, π] sont certaines lois discrètes πn,r (r est premier et divise n), et que les décompositions en facteurs premiers étudiées dans [5] constituent toutes les décompositions possibles (en facteurs premiers).1 De ces décompositions se déduisent toutes les propriétés de divisibilité de m.2 Nous développons ce point de vue et posons des problèmes analogues pour le cas de la circonférence γ.
Time-series analysis of tides and similar motions of the sea surface
Authors: Cartwright D. E.
Published: April 2006

This survey article, most of whose results are described in greater detail in Munk and Cartwright (1966), which will hereafter be abbreviated to MC, describes methods which aim to separate the response of the sea level at a given place due to various exciting forces such as gravity, solar radiation, non-linear effects, and weather. In so doing, it provides predictors for sea level which are formally simpler and somewhat more accurate than those given by the classical methods.
Some results on regular variation for distributions in queueing and fluctuation theory
Authors: Cohen J. W.
Published: April 2006

For the distribution functions of the stationary actual waiting time and of the stationary virtual waiting time of the GI/G/l queueing system it is shown that the tails vary regularly at infinity if and only if the tail of the service time distribution varies regularly at infinity.

For sn the sum of n i.i.d. variables xi, i = 1, …, n it is shown that if E {x1} < 0 then the distribution of sup, s1s2, …] has a regularly varying tail at + ∞ if the tail of the distribution of x1 varies regularly at infinity and conversely, moreover varies regularly at + ∞.

In the appendix a lemma and its proof are given providing necessary and sufficient conditions for regular variation of the tail of a compound Poisson distribution.
Shock models with underlying birth process
Authors: A-Hameed M. S. , Proschan F.
Published: April 2006

This paper extends results of Esary, Marshall and Proschan (1973) and A-Hameed and Proschan (1973). We consider the life distribution of a device subject to a sequence of shocks occurring randomly in time according to a nonstationary pure birth process: given k shocks have occurred in [0, t], the probability of a shock occurring in (t, t + Δ] is λ kλ (t)Δ + o (Δ). We show that various fundamental classes of life distributions (such as those with increasing failure rate, or those with the ‘new better than used' property, etc.) are obtained under appropriate assumptions on λ k, λ (t), and on the probability of surviving a given number of shocks.
A note on the Lévy distance
Authors: Thompson J. W.
Published: April 2006

The Lévy distance, L(F,G), between two distribution functions F and G has the important property that convergence of L(Fn,F) is equivalent to convergence in distribution. The fact that L(F,G) is not invariant under a change of scale has been thought to be a disadvantage. However, simple bounds on the Lévy distance between the transformed distribution functions can be found.
On the busy period of the modified GI/G/1 queue
Authors: Pakes A. G.
Published: April 2006

Proceeding from duality results for the GI/G/1 queue, this paper obtains the probability of the number served in a busy period of a GI/G/1 system where customers initiating a busy period have a different service time distribution from other customers. Using duality arguments for processes with interchangeable increments, the Laplace transform of the busy period duration is found for a modified GI/M/1 queue.
Estimation of transition probabilities in a multiparticle semi-Markov system
Authors: Burman David
Published: April 2006

Particles enter a finite-state system and move according to independent sample paths from a semi-Markov process. Strong limit theorems are developed for the ratio of the flow of particles from states i to j and the flow out of When the cumulative arrival of particles into the system up to time t, A (t) ∼ λtα, then a.s. When A (t)∼ λekt, then the flow between states must be normalized by the Laplace–Stieltjes transform of the conditional holding time distribution, in order to make the ratio an unbiased estimator of ρij.
Limit theorems for thinning of renewal point processes
Authors: L. Råde
Published: April 2006

Limit theorems for the thinning of renewal point processes according to two different schemes are studied. In the first scheme when a point is retained a random number of succeeding points are deleted. According to the second scheme a random number of points are deleted by an inhibitory Poisson process.
The infinite server queue with semi-Markovian arrivals and negative exponential services
Authors: Neuts Marcel F. , Chen Shun-Zer
Published: April 2006

The queue with an infinite number of servers with a semi-Markovian arrival process and with negative exponential service times is studied. The queue length process and the type of the last customer to join the queue before time t are studied jointly, both in continuous and in discrete time. Limiting stationary probabilities are also obtained.
Optimal issuing policies for non-identical units with stochastic lifetimes
Authors: Enns E. G. , Ehlers P. F.
Published: April 2006

Two non-identical units are to be issued sequentially. The optimal policy determines the issuing sequence which maximizes the expected lifetime of the pair of units. The units each have non-decreasing hazard rates which depend on whether the unit is in service or in storage. Sufficient conditions are obtained for optimal issuing policies in a variety of examples.
Signalling over a Gaussian channel with feedback and autoregressive noise
Authors: Wolfowitz J.
Published: April 2006

We study in detail the case of first-order regression, but our results can be extended to the general regression in a straightforward manner. An average energy constraint ((1.2) below) is imposed on each signal. In Section 2 we give an optimal linear signalling scheme (definition and proof in Section 4) for this channel. We conjecture that this scheme is optimal among all signalling schemes. Then the capacity C of the channel is (see Section 5) – log b, where b is the unique positive root (in x) of the equation x2 = (1 + g2(1 + |α|x)2)–1. Here a is the regression coefficient, and g2 is the ratio of the average energy per signal to the variance of the noise. An equivalent expression is C = ½log(1 + g2(1 + |α| b)2).
Multidimensional age-dependent branching processes allowing immigration: The limiting distribution
Authors: Kaplan Norman
Published: April 2006

This paper continues the author's study of age-dependent branching processes allowing immigration. In this paper the multidimensional case is considered. A sufficient condition is obtained for the existence of a legitimate limiting distribution. Several corollaries are obtained, which generalize many of the results of the discrete theory and those of the one-dimensional continuous time model.
Nearest-neighbour systems: a lemma with application to Bartlett's global solutions
Authors: Besag J. E.
Published: April 2006

Bartlett has proposed two alternative forms of spatial-temporal Markov model, each leading to the standard spatial equilibrium distribution for nearest-neighbour systems on a multi-dimensional lattice. The validity of one of these forms is discussed with the aid of a lemma.
Note on a clustering problem
Authors: Saperstein B.
Published: April 2006

Consider the clustering statistic, k* defined to be the maximum number of 1's to appear within any m consecutive positions in a random arrangement of a 1's and M–a 0's. Pr(k* – k) was found for the case k ≧ ½ a by the author [4], and then for m/M = 1/L, L an integer, by Naus [3]. Here, we generalise Naus's method to obtain the distribution of k* under no special restrictions on a, k, m or M.
The stochastic geyser problem for sample quantiles
Authors: Book Stephen A.
Published: April 2006

Consider a sequence of observations Yk = Xk + ek, where {Xk : 1 ≦ k < ∞} are i.i.d. random variables having distribution function F and {ek : 1 ≦ k < ∞} are arbitrary random errors of observation. The stochastic geyser problem asks for conditions under which F can be uniquely determined from a knowledge of the sequence of Yk's. The objective of the present article is to show that, if F is continuous and strictly increasing and the sample quantiles of successive blocks {Xn+ 1Xn+ 2, …, Xn+ K} of particular lengths K can be a.s. estimated to within an error of size o(1) as K →∞, then we can almost surely determine F from a single realization of {Yk : 1 ≦ k < ∞}.
Extinction probability for critical age-dependent branching processes with generation dependence
Authors: Fearn Dean H.
Published: April 2006

The limiting behavior of the probability of extinction of critical age-dependent branching processes with generation dependence is obtained using Goldstein's methods. Regularity conditions on the mean and variance of the birth distributions are assumed. Also the lifespan distribution is assumed to satisfy suitable regularity conditions.
Spitzer's condition for asymptotically symmetric random walk
Authors: Doney R. A.
Published: April 2006

If the step-length distribution function F for a random walk {Sn, n ≧ 0} is either continuous and symmetric or belongs to the domain of attraction of a symmetric stable law, then it is clear that the symmetric form of ‘Spitzer's condition' holds, i.e.

The question considered in this note is whether or not (⋆) can hold for other random walks. The answer is in the affirmative, for we show that (⋆) holds for a large class of random walks for which F is neither symmetric nor belongs to any domain of attraction; all such random walks are asymptotically symmetric, in the sense that limx→∞ {F(–x)| 1 – F(x)} = 1, but we show by an example that this is not a sufficient condition for (⋆) to hold.
Representation of the characteristic function of a stochastic integral
Authors: Riedel M.
Published: April 2006

Let X(t) be a continuous, homogeneous stochastic process with independent increments characterized by a, σ, M, N in the Lévy representation formula. In this note we obtain the Lévy canonical representation of the characteristic function of a stochastic integral (in the sense of convergence in probability) of the form

(where υ(t) is a non-decreasing, non-negative and left-continuous function) in terms of υ(t), a, σ, M, N.
The lengths of fragments covering a fixed marker in randomly cut linear or circular DNA
Authors: Litwin Samuel
Published: April 2006

A linear DNA molecule may be labelled at a fixed locus by a minute complementary radioactive molecule. A collection of identical molecules is to be so labelled and each one independently cut at a random number, N, of random places, X (N Poisson, X uniform). Fragments containing the label are to be collected and assayed by length. It is shown that the recovery pattern (fragment length distribution) contains a jump discontinuity at the fixed locus and may be used to determine the distance between the attachment site and the nearest end of the molecule.

The recovery pattern under the hypothesis that the collection of molecules are circularly permuted, i.e. the labelled locus is uniformly distributed over the length of the molecule, does not contain such discontinuities. The case where the labelling molecule has a non-negligible extent is also treated.
Criteria for ergodicity, exponential ergodicity and strong ergodicity of Markov processes
Authors: Tweedie R. L.
Published: April 2006

For regular Markov processes on a countable space, we provide criteria for the forms of ergodicity in the title in terms of the existence of solutions to inequalities involving the Q-matrix of the process. An application to birth-death processes is given.
Dependent thinning of point processes
Authors: Isham Valerie
Published: April 2006

A point process, N, on the real line, is thinned using a k -dependent Markov sequence of binary variables, and is rescaled. Second-order properties of the thinned process are described when k = 1. For general k, convergence to a compound Poisson process is demonstrated.
Continuous-time stochastic models of a multigrade population
Authors: McClean Sally I.
Published: April 2006

The continuous-time Markov model of a multigrade organization is extended in several ways. Firstly the internal transitions and the leaving process are generalized to a semi-Markov formulation which allows for the inclusion of well-authenticated leaving distributions such as the mixed exponential distribution. The previous assumption of Poisson recruitment is then generalized to allow for a time-dependent Poisson arrival distribution in which the instantaneous probability of an arrival is a mixture of exponential terms. Finally we extend the capital-related manpower model to describe a multigrade organization.
Criteria for strong ergodicity of Markov chains
Authors: Isaacson Dean , Tweedie Richard L.
Published: April 2006

For finite Markov chains, the concepts of ergodicity and strong ergodicity are equivalent, but this is not necessarily the case when the state space is infinite. In this note we give some new characterizations of strong ergodicity. These lead to simple necessary or sufficient criteria for strong ergodicity, which readily enable us to classify a number of examples.
Optimal replacement of damaged devices
Authors: Abdel-Hameed M. , Shimi I. N.
Published: April 2006

A device is subject to a sequence of shocks occurring randomly at times n = 1, 2, ⃛. At each point in time, shocks occur according to a Poisson distribution with parameter λ. Shocks cause damage and damage accumulates additively. They can cause the device to fail, and the probability of such a failure depends on the accumulated damage. Failure occurs because of shocks and can occur only at times n = 1, 2, ⃛. The device can be replaced before or at failure. If the device fails it is immediately replaced at a fixed cost. Replacement before failure can only occur at times n = 1, 2, ⃛, and is done at a lower cost depending on the amount of accumulated damage at replacement. In this paper we determine the optimal replacement policy that minimizes the expected cost per unit time.
On strong mixing and Leadbetter's D condition
Authors: Chernick Michael R.
Published: April 2006

Strong mixing is a condition which is often assumed to prove limit theorems for strictly stationary processes. Leadbetter's condition D(un) is used to prove limit theorems for maxima of stationary processes.

A sufficient condition for strong mixing to hold is given for the case where the process satisfies a pth-order Markov property. This condition can be easy to check for when p is small. This point is illustrated by two examples of first-order autoregressive processes.

The condition D(un) is shown to hold for any stationary Markov process.
Chaînes colorées: trois extensions d'une formule de P. Nelson
Authors: Letac Gérard
Published: April 2006

Nelson [9], [10] has computed the generating function of return probabilities to the initial state for a particular Markov chain on permutations of three objects. The formula obtained is

The present paper studies three distinct Markov chains generalizing the Nelson chain: the so-called three-coloured chain, with some birth-and-death processes on ℤ as a particular case, a chain on a graph close to the graph of the edges of a cube, and the daisy library. Two other themes piece together these chains: the notion of coloured chain and the technique of computation by additive processes.
Strong ergodicity for continuous-time Markov chains
Authors: Isaacson Dean , Arnold Barry
Published: April 2006

The concept of strong ergodicity for discrete-time homogeneous Markov chains has been characterized in several ways (Dobrushin (1956), Lin (1975), Isaacson and Tweedie (1978)). In this paper the characterization using mean visit times (Huang and Isaacson (1977)) is extended to continuous-time Markov chains. From this it follows that for a certain subclass of continuous-time Markov chains, X(t), is strongly ergodic if and only if the associated embedded chain is Cesaro strongly ergodic.
Levels of null persistency for Markov chains
Authors: Isaacson Dean , Colwell Peter
Published: April 2006

In the study of null-persistent Markov chains the sequence plays an important role. (See for example, Orey (1971), Athreya and Ney (1980).) In this paper we consider the rate of growth of UN to ∞ as N → ∞. This rate of growth is related to the rate of growth of as N → ∞ and also to the rate at which as n → ∞.
The stationary moments of Poisson-driven non-linear dynamical systems
Authors: Smith Charles E. , Cobb Loren
Published: April 2006

Moment recursion relations have previously been derived for the stationary probability density functions of continuous-time stochastic systems with Wiener (white noise) input. These results are extended in this paper to the case of Poisson (shot noise) input. The non-linear dynamical systems are expressed, in general, as stochastic differential equations, with an independent increment input. The transition probability density function evolves according to the appropriate Kolmogorov equation. Moments of the stationary density are obtained from the Fourier transform of the stationary density. The moment relations can be used to estimate the parameters of linear and non-linear stochastic systems from empirical moments, given either Wiener or Poisson input.
Wiener–Hermite expansion of a process generated by an Itô stochastic differential equation
Authors: Isobe Etsuo , Sato Shunsuke
Published: April 2006

In this paper we deal with the Wiener–Hermite expansion of a process generated by an Itô stochastic differential equation. The so-called Wiener kernels which appear in the functional series expansion are expressed in terms of the transition probability density function of the process.
On the stochastic ordering of waiting times for patterns in sequences of random digits
Authors: Blom Gunnar
Published: April 2006

Random digits are collected one at a time until a pattern with given digits is obtained. Blom (1982) and others have determined the mean waiting time for such a pattern. It is proved that when a given pattern has larger mean waiting time than another pattern, then the waiting time for the former is stochastically larger than that for the latter. An application is given to a coin-tossing game.
Counting figures in planar random configurations
Authors: Kellerer A. M.
Published: April 2006

Random configurations are considered that are generated by a Poisson process of figures in the plane, and a recent result is used to derive formulae for the estimation of the number of figures, and their mean area and perimeter. The formulae require merely the determination of the area, the perimeter, and the Euler–Poincaré characteristic of the random configurations in a fixed field of view. There are no similar formulae for the standard deviations of the estimates; their magnitudes in typical cases are therefore assessed by Monte Carlo simulations.
On the moments of some first-passage times
Authors: Stefanov Valeri T.
Published: April 2006

Let {Xt}t≧0 (t may be discrete or continuous) be a random process whose finite-dimensional distributions are of exponential type. The first-passage time inf{t:Xt≧f(t)}, where f(t) is a positive, continuous function, such that f(t)= o(t) as t↑∞, is considered. The problem of finiteness of its moments is solved for both the case that {Xt}t≧0 has stationary independent increments as well as the case in which no assumptions are made about stationarity and independence for the increments of the process. Applications to sequential estimation are also given.
The total progeny of a simple branching process with state-dependent immigration
Authors: Kulkarni M. V. , Pakes A. G.
Published: April 2006

The paper establishes limit theorems for the total progeny of a simple branching process in which immigration is allowed whenever the population size reaches 0.
Some duality results for a class of multivariate semi-markov processes
Authors: Janssen J. , Reinhard J. M.
Published: April 2006

The duality results well known for classical random walk and generalized by Janssen (1976) for (J-X) processes (or sequences of random variables defined on a finite Markov chain) are extended to a class of multivariate semi-Markov processes. Just as in the classical case, these duality results lead to connections between some models of risk theory and queueing theory.
On ross's conjectures about queues with non-stationary poisson arrivals
Authors: Heyman D. P.
Published: April 2006

Ross (1978) conjectured that the average delay in a single-server queue is larger when the arrival process is a non-stationary Poisson process than when it is a stationary Poisson process with the same rate. We present an example where equality obtains. When the number of waiting-positions is finite, Ross conjectured that the proportion of lost customers is greater in the nonstationary case. We present a counterexample to this conjecture.
Non-linear ESS models and polymorphism
Authors: Hines W. G. S. , Haigh John
Published: April 2006

Extensions of ESS theory to situations well outside the classical formulation often assume, as a convenience, that the population being modelled is, in some sense, monomorphic. While this assumption is in keeping with the original approach used in developing the theory, it is rendered less plausible by the observation that the original models do not preclude the possibility of polymorphism, a potentially serious omission. We consider a generalisation of the classical bilinear fitness function, and examine the circumstances that will tend to favour monomorphism.
Individually optimal routing in parallel systems
Authors: Kumar P. R. , Walrand J.
Published: April 2006

Jobs arrive at a buffer from which there are several parallel routes to a destination. A socially optimal policy is one which minimizes the average delay of all jobs, whereas an individually optimal policy is one which, for each job, minimizes its own delay, with route preference given to jobs at the head of the buffer. If there is a socially optimal policy for a system with no arrivals, which can be implemented by each job following a policy γ in such a way that no job ever utilizes a previously declined route, then we show that such a γ is an individually optimal policy for each job. Moreover γ continues to be individually optimal even if the system has an arbitrary arrival process, subject only to the restriction that past arrivals are independent of future route-traversal times. Thus, γ is an individually optimal policy which is insensitive to the nature of the arrival process. In the particular case where the times to traverse the routes are exponentially distributed with a possibly different mean time for each of the parallel routes, then such an insensitive individually optimal policy does in fact exist and is moreover trivially determined by certain threshold numbers. A conjecture is also made about more general situations where such individually optimal policies exist.
A characterization of the Poisson process
Authors: Gupta Pushpa Lata , Gupta Ramesh C.
Published: April 2006

Denoting by v(t) the residual life of a component in a renewal process, Çinlar and Jagers (1973) and Holmes (1974) have shown that if E(v(t)) is independent of t for all t, then the process is Poisson. In this note we prove, under mild conditions, that if E(G(v(t))) is constant, then the process is Poisson. In particular if E((v(t))r) for some specific real number r ≧ 1 is independent of t, then the process is Poisson.
Server utilization factors in queueing loss systems with ordered entry and heterogeneous servers
Authors: Pourbabai Behnam , Sonderman David
Published: April 2006

Approximation expressions for the server utilization factor of each server in a heterogeneous-server G/G/n queueing loss system with ordered entry are derived. The system is assumed to face a stationary counting process. Service times are generally distributed with possibly different service rates. The numerical results from this approximation method are then compared with those from a simulation study.
Embedding sequences of successive maxima in extremal processes, with applications
Authors: Ballerini Rocco , Resnick Sidney I.
Published: April 2006

Consequences of embedding sequences {Mn} in an extremal-F process are discussed where Mn represents the maximum of n independent (but not necessarily identically distributed) random variables. Various limit theorems are proved for the sample record rate, record times, inter-record times, and record values. These results are illustrated with applications to three particular record models: the Yang (1975) record model where population size increases geometrically, a record model where linear improvement is present, and a record model incorporating features of the previous two.
Probabilities of choosing applicants of arbitrary rank in the secretary problem
Authors: Rogerson Peter A.
Published: April 2006

Gilbert and Mosteller (1966) derive the probability of obtaining the best secretary when a fixed number of potential employees of varying quality are interviewed sequentially by an employer. This paper extends these results by deriving the probability of selecting an applicant of arbitrary rank under a variety of circumstances concerning the objective of employers and the amount of information employers have about applicant quality.
Stochastic differential equations for ruin probabilities
Authors: Møller Christian Max
Published: April 2006

The present paper proposes a general approach for finding differential equations to evaluate probabilities of ruin in finite and infinite time. Attention is given to real-valued non-diffusion processes where a Markov structure is obtainable. Ruin is allowed to occur upon a jump or between the jumps. The key point is to define a process of conditional ruin probabilities and identify this process stopped at the time of ruin as a martingale. Using the theory of marked point processes together with the change-of-variable formula or the martingale representation theorem for point processes, we obtain differential equations for evaluating the probability of ruin.

Numerical illustrations are given by solving a partial differential equation numerically to obtain the probability of ruin over a finite time horizon.
Models of superinfection and acquired immunity to multiple parasite strains
Authors: Milligan P. J. M. , Downham D. Y.
Published: April 2006

Individuals in communities in which different strains of pathogen are circulating can acquire resistance by accumulating immunity to each strain. After considering susceptibility, models of infection and immunity are defined for vector-borne diseases such as malaria and trypanosomiasis. For these models the prevalence of infection, the number of infections per individual, and the mean duration of infection, increase rapidly in young individuals, but decrease in older individuals as immunity is acquired to the various strains of pathogen; the mean interval between successive infections lengthens with age. The bivariate Poisson distribution is shown to be a close approximation to some stochastic processes. The models explain observed cross-sectional patterns of age prevalence, and longitudinal patterns in which individuals typically continue to become infected as they age, albeit with decreasing frequency. In these models the time spent infected depends on parasite diversity, as well as the inoculation and recovery rates. It is shown that control measures can cause an increase in the number of infections and the prevalence of infection in older individuals, and in the average prevalence in the community, even when strain-specific immunity is life-long.
On the limit behaviour of a superadditive bisexual Galton–Watson branching process
Authors: Gonzalez M. , Molina M.
Published: April 2006

The asymptotic behaviour of a superadditive bisexual Galton–Watson branching process is studied. Sufficient conditions for the almost sure and L1 convergence of the suitably normed process are given. Finally, a first approach to the study of the L1 convergence for a superadditive bisexual Galton–Watson branching process under the Z log+Z condition is considered.
On defining long-range dependence
Authors: Heyde C. C. , Yang Y.
Published: April 2006

Long-range dependence has usually been defined in terms of covariance properties relevant only to second-order stationary processes. Here we provide new definitions, almost equivalent to the original ones in that domain of applicability, which are useful for processes which may not be second-order stationary, or indeed have infinite variances. The ready applicability of this formulation for categorizing the behaviour for various infinite variance models is shown.
An invariant-sum characterization of Benford's law
Authors: Allaart Pieter C.
Published: April 2006

The accountant Nigrini remarked that in tables of data distributed according to Benford's law, the sum of all elements with first digit d (d = 1, 2,· ··, 9) is approximately constant. In this note, a mathematical formulation of Nigrini's observation is given and it is shown that Benford's law is the unique probability distribution such that the expected sum of all elements with first digits d1, · ··, dk is constant for every fixed k.