bluuebunny/crossref_metadata_2025_split huggingface dataset:
A stochastic model for the formation of a planetary system
Authors: Galley S. J. 
Published: July 2016

Summary
The stochastic model consists of a two-dimensional random walk with unit steps, each step being a Bernoulli trial. Two sets of possible conditions arising from astronomical theory give rise to two different barriers in the plane of the walk which cause a return to the origin. Another barrier indicates the formation of a planet and also causes a return to the origin. Consideration of the composition of the planets formed at this barrier allows their orbital distances and direction of rotation to be calculated. The predictions of one of the two models were found to be in close agreement with the observed planetary distances and masses in the solar system.
On the optimal control of stationary diffusion processes with inaccessible boundaries and no discounting
Authors: Morton R. 
Published: July 2016

Summary
Because there are no boundary conditions, extra properties are required in order to identify the correct potential cost function. A solution of the Dynamic Programming equation for one-dimensional processes leads to an optimal solution within a wide class of alternatives (Theorem 1), and is completely optimal if certain conditions are satisfied (Theorem 2). Necessary conditions are also given. Several examples are solved, and some extension to the multidimensional case is shown.
Unrooted trees for numerical taxonomy
Authors: Dobson Annette J. 
Published: July 2016

It is common to represent taxonomic hierarchies of related objects (such as similar plant or animal species or languages of the same family) by rooted trees with labelled terminal vertices which represent the objects. The multivariate data comparing numerous characteristics of the objects is first reduced to indices of similarity (or more often of dissimilarity) between each pair of objects. These are used to classify the objects into groups which are then depicted on a tree.
This paper shows that an unrooted tree with labelled terminal vertices may provide a better representation of the relationships between the objects because the similarity indices are required to conform to fewer restrictions. Also for a given number of terminal vertices, there are fewer unrooted than rooted trees so that studies using probability distributions of trees or seeking the most suitable tree to represent the data are more practicable.
On the comparison of point processes
Authors: Deng Y. L. 
Published: July 2016

Several different orderings for the comparison of point processes have been introduced and their relationships discussed in Whitt [9], Daley [2] and Deng [4]. It is of some interest to know whether these orderings, in general, are preserved under various operations on point processes. Some results concerning limit operations were given in Deng [4].
In the present paper, we first further introduce some convex and concave orderings for counting processes, and survey the relationships among all orderings mentioned in [9], [4] and this paper. Then we focus our attention on the study of the conditions for the preservation of orderings under the operations of superposition, thinning, shift, and random change of time.
A construction for multi-modal processes, and a potential memory device
Authors: Whittle P. 
Published: July 2016

It is shown that if parameters occurring linearly in the transition intensity of a Markov process are replaced by their respective ‘Bayesian estimates' then the new process thus generated has an equilibrium distribution which is a mixture (over parameter values) of the original parametrised equilibrium distribution.
One effectively then has an extra state dependence in that one selects from a given class of transition rules those rules which are most consistent with the value of current state. The effect of this is thus to preserve the status quo, in that unlikely transitions are made even less likely. By this means one can construct processes which show several distinct and metastable modes of behaviour, and which can serve as models for memory devices.
Monotonicity property of t-step maintainable structures in three-grade manpower systems: a counterexample
Authors: Guerry M. A. 
Published: July 2016

In this paper the t-step maintainable regions Mt
are examined in a three-graded system under the following conditions: the total size of the system remains constant during each intermediate step, demotions do not occur and recruitment control is considered.
A counterexample, showing that the monotonicity property Mt
⊆ Mt

+1 does not exist in general, refutes the conjecture of Davies [3].
Invariant measures for Markov chains with no irreducibility assumptions
Authors: Tweedie R. L. 
Published: July 2016

Foster's criterion for positive recurrence of irreducible countable space Markov chains is one of the oldest tools in applied probability theory. In various papers in JAP and AAP it has been shown that, under extensions of irreducibility such as ϕ -irreducibility, analogues of and generalizations of Foster's criterion give conditions for the existence of an invariant measure π for general space chains, and for π to have a finite f-moment ∫π (dy)f(y), where f is a general function. In the case f ≡ 1 these cover the question of finiteness of π itself.
In this paper we show that the same conditions imply the same conclusions without any irreducibility assumptions; Foster's criterion forces sufficient and appropriate regularity on the space automatically. The proofs involve detailed consideration of the structure of the minimal subinvariant measures of the chain.
The results are applied to random coefficient autoregressive processes in order to illustrate the need to remove irreducibility conditions if possible.
Slepian models for X
2-processes with dependent components with application to envelope upcrossings
Authors: Lindgren Georg 
Published: July 2016

A Slepian model for the local behaviour near the level upcrossings of a x
2-process with dependent Gaussian components is presented. In case of independent components, this model is shown to take on a rather simple form, thereby simplifying earlier results by Aronowich and Adler.
The Slepian model is applied to the envelope of a stationary Gaussian process and used to approximate the probability of ‘empty' envelope upcrossings, i.e. the probability that an envelope upcrossing is not followed by a level crossing in the original process.
Dynamic multivariate mean residual life functions
Authors: Shaked Moshe , Shanthikumar J. George 
Published: July 2016

In this paper we introduce and study a dynamic notion of mean residual life (mrl) functions in the context of multivariate reliability theory. Basic properties of these functions are derived and their relationship to the multivariate conditional hazard rate functions is studied.
A partial ordering, called the mrl ordering, of non-negative random vectors is introduced and its basic properties are presented. Its relationship to stochastic ordering and to other related orderings (such as hazard rate ordering) is pointed out. Using this ordering it is possible to introduce a weak notion of positive dependence of random lifetimes. Some properties of this positive dependence notion are given.
Finally, using the mrl ordering, a dynamic notion of multivariate DMRL (decreasing mean residual life) is introduced and studied. The relationship of this multivariate DMRL notion to other notions of dynamic multivariate aging is highlighted in this paper.
A new approach to (s, S) inventory systems
Authors: Hu Jian-Qiang , Nananukul Soracha , Gong Wei-Bo 
Published: July 2016

In this paper, we consider period review (s, S) inventory systems with independent and identically distributed continuous demands and full backlogging. Using an approach recently proposed by Gong and Hu (1992), we derive an infinite system of linear equations for all moments of inventory level. Based on this infinite system, we develop two algorithms to calculate the moments of the inventory level. In the first one, we solve a finite system of linear equations whose solution converges to the moments as its dimension goes to infinity. In the second one, we in fact obtain the power series of the moments with respect to s and S. Both algorithms are based on some very simple recursive procedures. To show their efficiency and speed, we provide some numerical examples for the first algorithm.
(s, S) INVENTORY SYSTEMS; DYNAMIC RECURSIVE EQUATIONS; INFINITE LINEAR EQUATIONS; MACLAURIN SERIES
A uniform limit theorem and exponential limit law for critical multitype age-dependent branching processes
Authors: Goldstein Martin I. 
Published: July 2016

Let Z(t) ··· (Z
1(t), …, Zk
(t)) be an indecomposable critical k-type age-dependent branching process with generating function F(s, t). Denote the right and left eigenvalues of the mean matrix M by u and v respectively and suppose μ is the vector of mean lifetimes, i.e. Mu = u, vM = v.

It is shown that, under second moment assumptions,

uniformly for s ∈ ([0, 1]
k
of the form s = 1 – cu, c a constant. Here vμ is the componentwise product of the vectors and Q[u] is a constant.
This result is then used to give a new proof of the exponential limit law.
On the maximum and absorption time of left-continuous random walk
Authors: Pakes Anthony G. 
Published: July 2016

In a recent paper Green (1976) obtained some conditional limit theorems for the absorption time of left-continuous random walk. His methods require that in the driftless case the increment distribution has exponentially decreasing tails and that the same is true for a transformed distribution in the case of negative drift.
Here we take a different approach which will produce Green's results under minimal conditions. Limit theorems are given for the maximum as the initial position of the random walk tends to infinity.
Extended block replacement policy with used items
Authors: Tango Toshiro 
Published: July 2016

Block replacement policy, under which items are replaced at constant intervals of time and at failure, is wasteful because sometimes almost new items are also replaced. In order to eliminate this kind of waste, the following replacement policy is suggested.
(1) Items are exchanged for new items at time kT (k ··· 1, 2, …).
(2) If items fail in [(k – 1) T, kT – v), they are replaced by new items, and if in [kT – v, kT), they are replaced by used items.
The results of this ‘extended block replacement policy with used items' are studied for the Erlang lifetime distribution.
Correlation structure of teletraffic measurements from randomly-scanned calls arrival data
Authors: Lee P. A. 
Published: July 2016

In teletraffic measurements, a call arrival process is commonly studied using a method with time-uniform or periodic scanning. The information recorded is the number of calls arrived between the scannings, from which data the number of scans between two successive calls is obtained. These later numbers are used as a measure of the interarrival times.
For an exponential call arrival process, except in the case of Poisson scanning, all other scanning schemes yield the number of scans which are not independent in any two interarrival intervals. By treating the problem as an interaction of two stationary stochastic point processes, we determine the exact joint probability distribution of the number of scans in two adjacent and non-adjacent interarrival intervals. An explicit expression for the correlation coefficient is also obtained.
Longest common subsequences of two random sequences
Authors: Chvátal Vacláv , Sankoff David 
Published: July 2016

Summary
Given two random k-ary sequences of length n, what is f(n,k), the expected length of their longest common subsequence? This problem arises in the study of molecular evolution. We calculate f(n,k) for all k, where n ≦ 5, and f(n,2) where n ≦ 10. We study the limiting behaviour of n
–1
f(n,k) and derive upper and lower bounds on these limits for all k. Finally we estimate by Monte-Carlo methods f(100,k), f(1000,2) and f(5000,2).
Networks of queues with customers of different types
Authors: Kelly F. P. 
Published: July 2016

The behaviour in equilibrium of networks of queues in which customers may be of different types is studied. The type of a customer is allowed to influence his choice of path through the network and, under certain conditions, his service time distribution at each queue. The model assumed will usually cause each service time distribution to be of a form related to the negative exponential distribution.
Theorems 1 and 2 establish the equilibrium distribution for the basic model in the closed and open cases; in the open case the individual queues are independent in equilibrium. In Section 4 similar results are obtained for other models, models which include processes better described as networks of colonies or as networks of stacks. In Section 5 the effect of time reversal upon certain processes is used to obtain further information about the equilibrium behaviour of those processes.
The single-server queue with random service output
Authors: Boxma O. J. 
Published: July 2016

In this paper a problem arising in queueing and dam theory is studied. We shall consider a G/G*/1 queueing model, i.e., a G/G/1 queueing model of which the service process is a separable centered process with stationary independent increments. This is a generalisation of the well-known G/G/1 model with constant service rate.
Several results concerning the amount of work done by the server, the busy cycles etc., are derived, mainly using the well-known method of Pollaczek. Emphasis is laid on the similarities and dissimilarities between the results of the ‘classical’ G/G/1 model and the G/G*/1 model.
Optimal replacement with semi-Markov shock models
Authors: Feldman Richard M. 
Published: July 2016

Consider a system that is subject to a sequence of randomly occurring shocks; each shock causes some damage of random magnitude to the system. Any of the shocks might cause the system to fail, and the probability of such a failure is a function of the sum of the magnitudes of damage caused from all previous shocks.
The purpose of this paper is to derive the optimal replacement rule for such a system whose cumulative damage process is a semi-Markov process. This allows for both the time between shocks and the damage due to the next shock to be dependent on the present cumulative damage level.
Only policies within the class of control-limit policies will be considered; namely, policies with which no action is taken if the damage is below a fixed level, and a replacement is made if the damage is above that.
An example will be given illustrating the use of the optimal replacement rule.
On the normal convergence of a class of simple batch epidemics
Authors: Langberg Naftali A. 
Published: July 2016

A group of n susceptible individuals exposed to a contagious disease is considered. It is assumed that at each instant in time one or more susceptible individuals can contract the disease.
The progress of this epidemic is modeled by a stochastic process Xn
(t), t in [0,∞) representing the number of infective individuals at time t. It is shown that Xn
(t), with the suitable standardization and under a mild condition, converges in distribution as n → ∞to a normal random variable for all t in (0, t
0), where t
0 is an identifiable number.
Maintainable regions in a Markov manpower model
Authors: Davies G. S. 
Published: July 2016

We examine the geometry of regions of maintainable structures arising in a Markov manpower model. The regions are described in terms of convex hulls, and it is shown that for systems divided into two or three grades these regions form an increasing sequence. It is also shown that the monotonie property fails quite drastically for a four-graded system.
An open problem is discussed for a related model.
A closure characterisation of phase-type distributions
Authors: Maier Robert S. , O'Cinneide Colm Art 
Published: July 2016

We characterise the classes of continuous and discrete phase-type distributions in the following way. They are known to be closed under convolutions, mixtures, and the unary ‘geometric mixture' operation. We show that the continuous class is the smallest family of distributions that is closed under these operations and contains all exponential distributions and the point mass at zero. An analogous result holds for the discrete class.
We also show that discrete phase-type distributions can be regarded as ℝ+-rational sequences, in the sense of automata theory. This allows us to view our characterisation of them as a corollary of the Kleene–Schützenberger theorem on the behavior of finite automata. We prove moreover that any summable ℝ+-rational sequence is proportional to a discrete phase-type distribution.
Burgers' equation by non-local shot noise data
Authors: Surgailis Donatas , Woyczynski Wojbor A. 
Published: July 2016

We study the scaling limit of random fields which are solutions of a non-linear partial differential equation, known as the Burgers equation, under stochastic initial conditions. These are assumed to be of a non-local shot noise type and driven by a Cox process. Previous work by Bulinskii and Molchanov (1991), Surgailis and Woyczynski (1993a), and Funaki et al. (1994) concentrated on the case of local shot noise data which permitted use of techniques from the theory of random fields with finite range dependence. Those are not available for the non-local case being considered in this paper.
Burgers' equation is known to describe various physical phenomena such as non-linear and shock waves, distribution of self-gravitating matter in the universe, and other flow satisfying conservation laws (see e.g. Woyczynski (1993)).
Some new integral geometric formulae, with stochastic applications
Authors: Miles R. E. 
Published: July 2016

Alternative forms of the integral geometric density of an r-subspace [r-flat] containing q[q + 1] points in euclidean n-space Rn
are given Stochastic applications in R3
include formulae for
(i) the mean area of intersection of a domain by an isotropic plane through the origin; and
(ii) the variance of the area of intersection of a domain by an isotropic uniform plane.
Interconnected birth and death processes
Authors: Puri Prem S. 
Published: July 2016

SummaryTwo cases of multiple linearly interconnected linear birth and death processes are considered. It is found that in general the solution of the Kolmogorov differential equations for the probability generating function (p.g.f)gof the random variables involved is not obtainable by standard methods, although one can obtain moments of the random variables from these equations. A method is considered for obtaining an approximate solution forg.This is based on the introduction of a sequence of stochastic processes such that the sequence {f(n)} of their p.g.f.'s tends togasn → ∞in an appropriate manner. The method is applied to the simple case of two birth and death processes with birth and death rates λiandμi, i =1,2, interconnected linearly with transition rates v andδ(see Figure 2). For this case some limit theorems are established and the probability of ultimate extinction of both the processes is considered. In addition, for the special cases (i) λ1=δ= 0, with the remaining rates time dependent and (ii) λ2=δ= 0, with the remaining rates constant, explicit solutions forgare obtained and studied.
Analytic characterization of the optimal control of a queueing system
Authors: Zacks S. , Yadin M. 
Published: July 2016

Summary
In a recent paper [7] the authors studied the optimal control policy of the following queueing system. Customers arrive at a service station according to a time homogeneous Poisson process with a known arrival intensity, λ. The service time at the station is a random variable having a negative exponential distribution with intensity μ, which is under control and can be varied over a certain range, according to the management policy.
A process with chain dependent growth rate
Authors: Keilson Julian , Rao S. Subba 
Published: July 2016

Additive processes on finite Markov chains have been investigated by Miller ([8], [9]), Keilson and Wishart ([2], [3], [4]) and by Fukushima and Hitsuda [1]. These papers study a two-dimensional Markov Process {X(t),R(t)} whose state space isR1× {1, 2, ···,R} characterized by the following properties:(i)R(t) is an irreducible Markov chain on states 1,2, …,R governed by atransition probability matrixBo= {brs}.(ii)X(t) is a sumof random increments dependent on the chain, i.e., if the ith transition takes the chain from state r to state s, then the incrementhas the distribution(iii)Nt, is t in discrete time while in the continuous time case Nt, might be an independent Poisson process.
On the distribution and moments of the strength of a bundle of filaments
Authors: Suh M. W. , Bhattacharyya B. B. , Grandage A. 
Published: July 2016

Summary
Small sample and large sample properties of the bundle strength of parallel filaments studied earlier by Daniels (1945) and Sen, Bhattacharyya, Suh (1969) have been developed here by probabilistic argument. The statistics belong to a family or class of statistics, each of which forms a reverse semi-martingale sequence. Certain moment properties are also discussed.
Expenditure patterns for risky R and D projects
Authors: Kamien Morton I. , Schwartz Nancy L. 
Published: July 2016

Summary
In this paper we derive the time pattern of optimal planned expenditures for R and D projects in which the total effort required to complete the research satisfactorily is not known. Theorem 1 summarizes our results under alternative assumptions regarding the behavior of the function governing the supposed probability of completing the R and D satisfactorily with incremental effort. In addition, an easily employed necessary condition for the R and D project to be worthwhile is provided in Theorem 2.
On an extension of Gani's model for attachment of phages to bacteria
Authors: Bhat B. R. 
Published: July 2016

Summary
In recent papers Yassky (1962) and Gani (1965) have considered respectively deterministic and stochastic models for the attachment of phages to bacteria. Following Brenner's (1965) conjecture they assumed that there is a maximum, S (say), to the number of phages that can be attached to a bacterium. In this note, Gani's (1965) results will be obtained starting from a different set of assumptions. This modification enables us to consider the case when S is a random variable, which probably is a more realistic assumption. Some remarks on the problem of estimation for the latter model are given in Section 3.