bluuebunny/crossref_metadata_2025 huggingface dataset:
Evaluation of the decay parameter for some specialized birth-death processes
Authors: Kijima Masaaki
Published: July 2016

Let N(t) be an exponentially ergodic birth-death process on the state space {0, 1, 2, ···} governed by the parameters {λn, μn
}, where µ
0 = 0, such that λn
= λ and μn
= μ for all n ≧ N, N ≧ 1, with λ < μ. In this paper, we develop an algorithm to determine the decay parameter of such a specialized exponentially ergodic birth-death process, based on van Doorn's representation (1987) of eigenvalues of sign-symmetric tridiagonal matrices. The decay parameter is important since it is indicative of the speed of convergence to ergodicity. Some comparability results for the decay parameters are given, followed by the discussion for the decay parameter of a birth-death process governed by the parameters such that lim
n→∞
λn
= λ and lim
n→∞
µn
= μ. The algorithm is also shown to be a useful tool to determine the quasi-stationary distribution, i.e. the limiting distribution conditioned to stay in {1, 2, ···}, of such specialized birth-death processes.
Convex hulls of selected subsets of a Poisson process
Authors: Blackwell Paul
Published: July 2016

This paper considers sets of points from a Poisson process in the plane, chosen to be close together, and their properties. In particular, the perimeter of the convex hull of such a point set is investigated. A number of different models for the selection of such points are considered, including a simple nearest-neighbour model. Extensions to marked processes and applications to modelling animal territories are discussed.
Some results on block replacement policies and renewal theory
Authors: Shaked Moshe , Zhu Haolong
Published: July 2016

Age and block replacement policies are commonly used in order to reduce the number of in-service failures. The focus in this paper is on the block replacement policies, about which relatively less is known than age replacement policies. Several new results which connect the properties of block replacement policies with the properties of the corresponding renewal function and the excess lifetimes are obtained. Some applications and the relationships between these new results and some known results are included.
Asymptotic variance parameters for the boundary local times of reflected Brownian motion on a compact interval
Authors: Williams R. J.
Published: July 2016

A direct derivation is given of a formula for the normalized asymptotic variance parameters of the boundary local times of reflected Brownian motion (with drift) on a compact interval. This formula was previously obtained by Berger and Whitt using an M/M/1/C queue approximation to the reflected Brownian motion. The bivariate Laplace transform of the hitting time of a level and the boundary local time up to that hitting time, for a one-dimensional reflected Brownian motion with drift, is obtained as part of the derivation.
Extremal properties of the shortest/longest non-full queue policies in finite-capacity systems with state-dependent service rates
Authors: Sparaggis P. D. , Towsley D. , Cassandras C. G.
Published: July 2016

We consider the problem of routing jobs to parallel queues with identical exponential servers and unequal finite buffer capacities. Service rates are state-dependent and non-decreasing with respect to queue lengths. We establish the extremal properties of the shortest non-full queue (SNQ) and the longest non-full queue (LNQ) policies, in systems with concave/convex service rates. Our analysis is based on the weak majorization of joint queue lengths which leads to stochastic orderings of critical performance indices. Moreover, we solve the buffer allocation problem, i.e. the problem of how to distribute a number of buffers among the queues. The two optimal allocation schemes are also ‘extreme', in the sense of capacity balancing. Some extensions are also discussed.
Rough limit results for level-crossing probabilities
Authors: Nyrhinen Harri
Published: July 2016

Let Y
1, Y
2, · ·· be a stochastic process and M a positive real number. Define TM
= inf{n | Yn
> M} (TM
= + ∞ if for n = 1, 2, ···)· We are interested in the probabilities P(TM
<∞) and in particular in the case when these tend to zero exponentially fast when M tends to infinity. The techniques of large deviations theory are used to obtain conditions for this and to find out the rate of convergence. The main hypotheses required are given in terms of the generating functions associated with the process (Yn
).
On a distributional bound arising in autoregressive model fitting
Authors: Papangelou F.
Published: July 2016

In the theory of autoregressive model fitting it is of interest to know the asymptotic behaviour, for large sample size, of the coefficients fitted. A significant role is played in this connection by the moments of the norms of the inverse sample covariance matrices. We establish uniform boundedness results for these, first under generally weak conditions and then for the special case of (infinite order) processes. These in turn imply corresponding ergodic theorems for the matrices in question.
A sample-path approach to Palm probabilities
Authors: Stidham Shaler
Published: July 2016

Previous papers have established sample-path versions of relations between marginal time-stationary and event-stationary (Palm) state probabilities for a process with an imbedded point process. This paper extends the use of sample-path analysis to provide relations between frequencies for arbitrary (measurable) sets in function space, rather than just marginal (one-dimensional) frequencies. We define sample-path analogues of the time-stationary and event-stationary (Palm) probability measures for a process with an imbedded point process, and then derive sample-path versions of the Palm transformation and inversion formulas.
Dynamic search for a moving target
Authors: Assaf David , Sharlin-Bilitzky Ariela
Published: July 2016

An object is hidden in one of two boxes and occasionally moves between the boxes in accordance with some specified continuous-time Markov process. The objective is to find the object with a minimal expected cost. In this paper it is assumed that search efforts are unlimited. In addition to the search costs, the ‘real time' until the object is found is also taken into account in the cost structure. Our main results are that the optimal policy may consist of five regions and that the controls applied should be of the extreme 0 or ∞ type. The resulting expected cost compares favorably with that of the expected cost with bounded controls studied previously in the search literature.
Analysis of the M
x/G/1 queue by N-policy and multiple vacations
Authors: Lee Ho Woo , Lee Soon Seok , Park Jeong Ok , Chae K. C.
Published: July 2016

We consider an Mx
/G/1 queueing system with N-policy and multiple vacations. As soon as the system empties, the server leaves for a vacation of random length V. When he returns, if the queue length is greater than or equal to a predetermined value N(threshold), the server immediately begins to serve the customers. If he finds less than N customers, he leaves for another vacation and so on until he finally finds at least N customers. We obtain the system size distribution and show that the system size decomposes into three random variables one of which is the system size of ordinary Mx
/G/1 queue. The interpretation of the other random variables will be provided. We also derive the queue waiting time distribution and other performance measures. Finally we derive a condition under which the optimal stationary operating policy is achieved under a linear cost structure.
The autocorrelation function of the queue length process for the two-server Poisson queue
Authors: Hill James M. , Tognetti Keith P.
Published: July 2016

Using Laplace transforms an explicit analytical expression is obtained for the autocorrelation function of the number in the system for the two-server Poisson queue. The method employed may be extended to Poisson queues with more than two servers.
The simple branching process: a note on convergence when the mean is infinite
Authors: Davies P. L.
Published: July 2016

Letdenote the simple branching process withZ0= 1 and letGdenote the distribution function ofZ1.SupposeGsatisfiesx−α−γ(x)≦1 −G(x) ≦x−α+γ(x)for largex, where (i) 0 < α < 1, (ii)γ(x) is non-negative and non-increasing, (iii)xγ(x)is non-decreasing and (iv)Then limn→∞αnlog (Zn+ 1) converges almost surely to a non-degenerate finite random variableWsatisfyingP(W= 0) =q= probability of extinction of theprocess.
On linearly increasing mean residual lifetimes
Authors: Morrison Donald G.
Published: July 2016

It is shown that the gamma distribution is the unique mixing distribution of exponentials that leads to a linearly increasing mean residual lifetime function. A corollary of this result is that regardless of the mixing process the Pareto distribution is the unique aggregate distribution mixture with this property.
A new look at the simple epidemic process
Authors: Billard L. , Lacayo H. , Langberg N. A.
Published: July 2016

Classical epidemic models have invariably proved to be mathematically intractable. By considering the distribution of the number of infectives in a simple epidemic process as a convolution of exponential waiting times, the solution to the classical model is obtained easily giving more insight into the underlying structure. The idea can be extended to other simple epidemic models.
An application of the Jordan canonical form to the epidemic problem
Authors: Gilbert Linda P. , Johnson A. M.
Published: July 2016

The stochastic version of the simple epidemic is considered in this paper. A method which has computational advantages is developed for computing the probability distribution of the process. The method is based on the Jordan canonical form of the matrix representing the system of differential-difference equations for the simple epidemic. It is also shown that the method can be applied to the general epidemic as well as any other right-shift process.
On the quantogram of Kendall and Kent
Authors: Csörgő Sándor
Published: July 2016

The ‘snake' theorem, i.e., the weak convergence of the complex quantogram, is studied. The moment assumption is weakened by a strong approximation result of the author.
The mixed exponential solution to the first-order autoregressive model
Authors: Lawrance A. J.
Published: July 2016

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.
Properties of the bivariate delayed Poisson process
Authors: Lawrance A. J. , Lewis P. A. W.
Published: July 2016

The bivariate Poisson point process introduced in Cox and Lewis (1972), and there called the bivariate delayed Poisson process, is studied further; the process arises from pairs of delays on the events of a Poisson process. In particular, results are obtained for the stationary initial conditions, the joint distribution of the number of operative delays at an arbitrary time, the asynchronous counting distribution, and two semi-synchronous interval distributions. The joint delay distribution employed allows for dependence and two-sided delays, but the model retains the independence between different pairs of delays.
Limits of compound and thinned point processes
Authors: Kallenberg Olav
Published: July 2016

Let η =Σ
j
δτj
be a point process on some space S and let β,β
1,β
2, … be identically distributed non-negative random variables which are mutually independent and independent of η. We can then form the compound point process ξ = Σ
j
β
j
δτj
which is a random measure on S. The purpose of this paper is to study the limiting behaviour of ξ as . In the particular case when β takes the values 1 and 0 with probabilities p and 1 –p respectively, ξ becomes a p-thinning of η and our theorems contain some classical results by Rényi and others on the thinnings of a fixed process, as well as a characterization by Mecke of the class of subordinated Poisson processes.
A queue with poisson input and semi-Markov service times: busy period analysis
Authors: Purdue Peter
Published: July 2016

We discuss here an extension of a queueing model studied by Neuts and also by Çinlar. We obtain a matrix form of Takács' equations and exhibit the equilibrium conditions. We also show that the conditions imposed by Neuts and by Çinlar in order to obtain their results concerning the busy period are not necessary.
Polynomial bounds for probability generating functions
Authors: Braun Henry
Published: July 2016

The problem of approximating an arbitrary probability generating function (p.g.f.) by a polynomial is considered. It is shown that if the coefficients rj
are chosen so that LN
(·) agrees with g(·) to k derivatives at s = 1 and to (N – k) derivatives at s = 0, then LN
is in fact an upper or lower bound to g; the nature of the bound depends only on k and not on N. Application of the results to the problems of finding bounds for extinction probabilities, extinction time distributions and moments of branching process distributions are examined.
Convergence of transport processes with radially symmetric direction changes, and chain molecules
Authors: Gorostiza Luis G.
Published: July 2016

When passing from two to more dimensions, the study of non-isotropic scattering transport processes, and chain molecules, which are both covered by the same mathematical model, becomes affected by the non-commutativity of rotations. The techniques developed in [2], together with results on radially symmetric direction changes, are used in this paper to obtain a functional central limit theorem for those random processes, with a suitable normalization, the limit being a Brownian motion process which is completely identified.
On possible rates of growth of age-dependent branching processes with immigration
Authors: Grey D. R.
Published: July 2016

It is shown that if ϕ is a given function out of a large class satisfying a certain regularity condition, then a supercritical age-dependent branching process {Z(t)} exists with deterministic immigration and given life-length and family-size distributions such that Z(t)/(eat ϕ(t)) converges in probability to a non-zero constant, a being the appropriate Malthusian parameter.

As an easy corollary one discovers the asymptotic behaviour of some processes with random immigration.
Two extreme value processes arising in hydrology
Authors: Karr Alan F.
Published: July 2016

Let Tn
be the time of occurrence of the nth flood peak in a hydrological system and Xn
the amount by which the peak exceeds a base level. We assume that ((Tn
, Xn
)) is a Poisson random measure with mean measure μ(dx) K(x, dy). In this note we characterize two extreme value processes which are functionals of ((Tn
, Xn
)). The set-parameterized process {MA
} defined by MA
= sup {Xn
:Tn
∈ A} is additive and we compute its one-dimensional distributions explicitly. The process (Mt
), where Mt
= sup{Xn
: Tn
≦ t}, is a non-homogeneous strong Markov process. Our results extend but computationally simplify those of previous models.
On the parity of individuals in a branching process
Authors: Gani J. , Saunders I. W.
Published: July 2016

This paper is concerned with the parity of a population of yeast cells, each of which may bud, not bud or die. Two multitype models are considered: a Galton-Watson process in discrete time, and its analogous birth-death process in continuous time. The mean number of cells with parity 0, 1, 2, … is obtained in both cases; some simple results are also derived for the second moments of the two processes.
The convergence of a position-dependent branching process used as an approximation to a model describing the spread of an epidemic
Authors: Radcliffe J.
Published: July 2016

A supercritical position-dependent Markov branching process has been used as an approximation to a model describing the initial geographical spread of a measles epidemic (Bartlett (1956)). Letαbe its Malthusian parameter,ßits velocity of propagation,Z(A,t) the number of individuals in the setAat timet,andA√(ßt)= [√(ßt)r:r ∈ A]. The mean square convergence of the random variableW(A, t)= e–αtZ(A√(ßt),t) to a limit variableW(A) is established.
The mean number of maxima above high levels in Gaussian random fields
Authors: Hasofer A. M.
Published: July 2016

An asymptotic formula for the mean number of maxima above a level of an n-dimensional stationary Gaussian field has been given by Nosko without proof. In this note a short general proof of this formula is given.
Averages for polygons formed by random lines in Euclidean and hyperbolic planes
Authors: Santaló L. A. , Yañez I.
Published: July 2016

We consider a countable number of independent random uniform lines in the hyperbolic plane (in the sense of the theory of geometrical probability) which divide the plane into an infinite number of convex polygonal regions. The main purpose of the paper is to compute the mean number of sides, the mean perimeter, the mean area and the second order moments of these quantities of such polygonal regions. For the Euclidean plane the problem has been considered by several authors, mainly Miles [4]–[9] who has taken it as the starting point of a series of papers which are the basis of the so-called stochastic geometry.
Stochastic asymptotic exponential stability of stochastic integral equations
Authors: Tsokos Chris P. , Hamdan M. A.
Published: July 2016

The object of this paper is to study the stochastic asymptotic exponential stability of a stochastic integral equation of the form

A random solution of the stochastic integral equation is considered to be a second order stochastic process satisfying the equation almost surely. The random solution, y(t, ω) is said to be. stochastically asymptotically exponentially stable if there exist some β > 0 and a γ > 0 such that for t∈ R
+.

The results of the paper extend the results of Tsokos' generalization of the classical stability theorem of Poincaré-Lyapunov.
The infinite server queue with semi-Markovian arrivals and negative exponential services
Authors: Neuts Marcel F. , Chen Shun-Zer
Published: July 2016

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.
Some theorems on the transient covariance of Markov chains
Authors: Reynolds John F.
Published: July 2016

Several authors have considered the covariance structure of continuous parameter Markov chains. Most of this work has dealt with particular process ses, notably Morse (1955) who analysed the simple M/M/1 queue and Bene-(1961) who considered a telephone trunking model. Furthermore, the results obtained apply only when the process has attained its limiting (stationary) distribution. A recent paper by Reynolds (1968) gave some general results for finite chains, still assuming stationarity. This note generalises the results obtained therein, and considers the covariance structure during the transient period prior to attaining the stationary distribution where this exists. In the case where no such distribution exists, the results are valid throughout the whole lifetime of the process.
A limit theorem for inter-record times
Authors: Shorrock R. W.
Published: July 2016

A limit theorem for inter-record times is obtained which seems to explain many of their known asymptotic properties. The process of inter-record times is shown to be approximately non-homogeneous Poisson.
The cost of a general stochastic epidemic
Authors: Gani J. , Jerwood D.
Published: July 2016

This paper is concerned with the cost Cis
= aWis
+ bTis
(a, b > 0) of a general stochastic epidemic starting with i infectives and s susceptibles; Tis
denotes the duration of the epidemic, and Wis
the area under the infective curve. The joint Laplace-Stieltjes transform of (Wis, Tis
) is studied, and a recursive equation derived for it. The duration Tis
and its mean Nis
are considered in some detail, as are also Wis
and its mean Mis
. Using the results obtained, bounds are found for the mean cost of the epidemic.
Conditional Poisson processes
Authors: Serfozo Richard F.
Published: July 2016

A conditional Poisson process (often called a double stochastic Poisson process) is characterized as a random time transformation of a Poisson process with unit intensity. This characterization is used to exhibit the jump times and sizes of these processes, and to study their limiting behavior. A conditional Poisson process, whose intensity is a function of a Markov process, is discussed. Results similar to those presented can be obtained for any process with conditional stationary independent increments.
Stochastic approximation for the general epidemic
Authors: Ludwig Donald
Published: July 2016

A system of equations is introduced whose solutions are remarkably close to corresponding solutions of the “general stochastic epidemic”. If N is the population size, then there are approximately equations to be solved for the general stochastic epidemic while the number of equations in the approximating system is proportional to N. An asymptotic approximation to the general stochastic epidemic is also introduced. Numerical comparisons of the stochastic and asymptotic approximations with the exact solution are presented.
Moments of age and remaining life in renewal processes
Authors: Katz S. , Naor P. , Shinnar R.
Published: July 2016

Expressions are developed for the moments of age and remaining life in renewal processes, and from them, expressions for the moments of the last and next renewal epochs. The results for remaining life and next renewal epoch may be regarded as generalizations of theorems of Wald (1944) and others. The results for age and last renewal epoch do not fit into this sequential analysis framework. Both sets of results are obtained from partial differential equations developed for the distributions of age and of remaining life. These partial differential equations are of the “conservation” type familiar from statistical mechanics, and may have some independent interest for renewal theory.
The equivalence of some overlapping and non-overlapping generation models for the study of genetic drift
Authors: Cannings C.
Published: July 2016

The paper discusses models for genetic drift in haploid models; non-overlapping models following Wright, and overlapping models following Moran. It is shown that these models, and their extensions by Chia and Watterson, can all be restated as non-overlapping models. This equivalence between the two sets of models greatly facilitates the specification of latent roots and vectors.
Results in the asymptotic and equilibrium theory of Poisson cluster processes
Authors: Westcott M.
Published: July 2016

This paper contains a detailed study of the Poisson cluster process on the real line, concentrating on two aspects; first, the asymptotic distribution of the number of points in [0,t) as t→ ∞ for both transient and equilibrium cluster processes and, secondly, a general formula for the probability generating function of the equilibrium process. Asymptotic formulae for cumulants of the process are also derived. The results obtained generalize those of previous writers. The approach is analytical, in contrast to the probabilistic treatment of P. A. W. Lewis.
A central limit theorem for exchangeable variates with geometric applications
Authors: Moran P. A. P.
Published: July 2016

A central limit theorem is proved for the sum of random variables Xr
all having the same form of distribution and each of which depends on a parameter which is the number occurring in the rth cell of a multinomial distribution with equal probabilities in N cells and a total n, where nN
–1 tends to a non-zero constant. This result is used to prove the asymptotic normality of the distribution of the fractional volume of a large cube which is not covered by N interpenetrating spheres whose centres are at random, and for which NV–

1 tends to a non-zero constant. The same theorem can be used to prove asymptotic normality for a large number of occupancy problems.
Non-stationary random set processes with application to pattern reconstruction
Authors: Moore Marc
Published: July 2016

Examples of non-stationary random set processes are presented. The reconstruction of a pattern, generated by such a process, is studied; a particular arrangement of the sample-points is considered.
Some comments on spectral representations of non-stationary stochastic processes
Authors: Tong H.
Published: July 2016

The first part of the paper gives a multitude of essentially different representations of a stationary stochastic process. The second part gives a sufficient condition for the sum of two oscillatory processes to be again oscillatory.
Limiting second moments for transient states of Markov chains
Authors: Wynn H. P.
Published: July 2016

The set of transient states of a Markov chain is considered as a system. If numbers of arrivals to the system at discrete time points have constant mean and covariance matrix then there is a limiting distribution of numbers in the states. Necessary and sufficient conditions are given for this distribution to yield zero correlations between states.
A limit theorem for priority queues in heavy traffic
Authors: Harrison J. Michael
Published: July 2016

A single server, two priority queueing system is studied under the heavy traffic condition where the system traffic intensity is either at or near its critical value. An approximation is developed for the transient distribution of the low priority customers' virtual waiting time process. This result is stated formally as a limit theorem involving a sequence of systems whose traffic intensities approach the critical value.
Total progeny in a multitype critical age dependent branching process with immigration
Authors: Weiner Howard J.
Published: July 2016

In a multitype critical age dependent branching process with immigration, the numbers of cell types born by t, divided by t
2, tends in law to a one-dimensional (degenerate) law whose Laplace transform is explicitily given. The method of proof makes a correspondence between the moments in the m-dimensional case and the one-dimensional case, for which the corresponding limit theorem is known. Other applications are given, a possible relaxation of moment assumptions, and extensions are indicated.
A central limit theorem for a security of supply model
Authors: Platz Ole
Published: July 2016

A security of supply model for energy is described. The energy demand is a non-random periodic function of time and the supply model is a continuous-time Markov chain. Asymptotic normality is proved for the two important reliability quantities: the amount of energy not supplied and the time the demand is not met within a time interval.
Remainder term estimate for the asymptotic normality of the number of renewals
Authors: Englund Gunnar
Published: July 2016

It is well known that the number of renewals in the time interval [0, t] for an ordinary renewal process is approximately normally distributed under general conditions. We give a remainder term estimate for this normal distribution approximation.
A simple proof of Whittle's bridging condition in dynamic programming
Authors: Hartley Roger
Published: July 2016

We offer a short proof that the bridging condition introduced by Whittle is sufficient for regularity in negative dynamic programming. We exploit concavity of the optimal value operator and do not need a special treatment of the case when optimal policies do not exist.
An exponential Markovian stationary process
Authors: Tavares L. Valadares
Published: July 2016

A new markovian process {X
i : i = 0, 1, 2, ·· ·} following a negative exponential distribution and with the same autocorrelation function as the lag-1 autoregressive process is proposed and studied in this paper. The exact distribution of the maxima and of the minima of n consecutive Xi
values are obtained and the exact expected upcrossing interval is given for any crossing level.
A random graph
Authors: Ross Sheldon M.
Published: July 2016

We consider an unordered graph where there is one arc emanating from each node. We suppose that the arc that emanates from i will go to j with probability Pj
. The probability that the resultant graph is connected and a recursive formula for the distribution of the number of components it possesses are derived.
Multiserver scheduling of jobs with increasing completion rates
Authors: Gittins J. C.
Published: July 2016

Under certain conditions it is shown that for jobs with increasing completion rates the expected flow time is minimised by a non-pre-emptive service discipline.
Survival under the pure birth shock model
Authors: Klefsjö Bengt
Published: July 2016

Suppose that a device is subjected to shocks and that denotes the probability of surviving k shocks. Then is the probability that the device will survive beyond t, where is the counting process which governs the arrival of shocks. A-Hameed and Proschan (1975) considered the survival function H(t) under what they called the pure birth shock model. In this paper we shall prove that is IFRA and DMRL under conditions which differ from those used by A-Hameed and Proschan (1975).
A bounded growth population subjected to emigrations due to population pressure
Authors: Trajstman A. C.
Published: July 2016

A model is presented for a bounded growth population subjected to random-sized emigrations that occur due to population pressure.

The deterministic growth component examined in detail is defined by a Prendiville process. Results are obtained for the times between emigration events and for the population increase between emigrations. Some information is obtained about the mean time to extinction and also for the mean population level when the emigration-size distribution is negative exponential.
Efficient simulation of tail probabilities of sums of dependent random variables
Authors: Blanchet Jose H. , Rojas-Nandayapa Leonardo
Published: July 2016

We study asymptotically optimal simulation algorithms for approximating the tail probability of P(e
X
1
+⋯+ e
X

d

>u) as u→∞. The first algorithm proposed is based on conditional Monte Carlo and assumes that (X
1,…,X

d
) has an elliptical distribution with very mild assumptions on the radial component. This algorithm is applicable to a large class of models in finance, as we demonstrate with examples. In addition, we propose an importance sampling algorithm for an arbitrary dependence structure that is shown to be asymptotically optimal under mild assumptions on the marginal distributions and, basically, that we can simulate efficiently (X
1,…,X

d
|X

j
>b) for large b. Extensions that allow us to handle portfolios of financial options are also discussed.
Maximization of a survival probability and its application
Authors: Mi Jie
Published: July 2016

When a mission is assigned, it often is the case that the component used to perform the task is required to work properly during the period of the mission time. In other words, the probability of the event that this component does not fail within the allowable mission time should be as large as possible. This problem is considered for the case when the lifetime of a component has a bathtub-shaped failure rate function, and it is found that burn-in procedure is beneficial. An application of this result to the problem of minimizing the mean number of failures in a given period of mission time is also considered.
Comparing sums of exchangeable Bernoulli random variables
Authors: Lefèvre Claude , Utev Sergey
Published: July 2016

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}.
Randomized multihit models and their identification
Authors: Hanin L. G. , Klebanov L. B. , Yakovlev A. Yu.
Published: July 2016

The multihit–one target model induces a stochastic ordering of cell survival with respect to the cell sensitivity characteristics. This property can be used for a description of cell killing effects in heterogeneous populations of cells on the basis of randomized versions of the model. In such versions, either the critical number of lesions or the mean number of hits per unit dose (sensitivity), or both, are assumed to be random. We give some new results specifying conditions under which the randomized multihit models are identifiable, with a focus on the following cases: (1) the critical number of radiation-induced lesions,m,is random; (2) the sensitivity parameter,x, is random givenmis known or otherwise; (3)xandmform a pair of independent random variables.
Heavy traffic analysis of a transportation network model
Authors: Peterson William P. , Wein Lawrence M.
Published: July 2016

We study a model of a stochastic transportation system introduced by Crane. By adapting constructions of multidimensional reflected Brownian motion (RBM) that have since been developed for feedforward queueing networks, we generalize Crane's original functional central limit theorem results to a full vector setting, giving an explicit development for the case in which all terminals in the model experience heavy traffic conditions. We investigate product form conditions for the stationary distribution of our resulting RBM limit, and contrast our results for transportation networks with those for traditional queueing network models.
Convergence properties of simulated annealing for continuous global optimization
Authors: Locatelli M.
Published: July 2016

In this paper conditions for the convergence of a class of simulated annealing algorithms for continuous global optimization are given. The previous literature about the subject gives results for the convergence of algorithms in which the next candidate point is generated according to a probability distribution whose support is the whole feasible set. A class of possible cooling schedules has been introduced in order to remove this restriction.
A Bayesian analysis of layered defense systems
Authors: Al-mutairi Dhaifalla K. , Al-khamis Talal M. , Abdel-Hameed Mohamed S.
Published: July 2016

A Bayesian approach for analyzing layered defense systems is presented. This approach incorporates the dependence of penetration probabilities on the size of attackers going into any layer. A general formula is developed for computing the predictive distribution of the number of attackers surviving any layer as well as the posterior distribution of the penetration probabilities under the a priori assumptions that: (i) the probabilities are dependent and their joint distribution is Dirichlet, and (ii) the probabilities are independent. Positive dependence of the penetration probabilities as well as the number of attackers surviving the different layers is also established.
Sooner waiting time problems in a sequence of trinary trials
Authors: Koutras M. V. , Alexandrou V. A.
Published: July 2016

Let X
1
, X
2
,· ·· be a (linear or circular) sequence of trials with three possible outcomes (say S, S∗ or F) in each trial. In this paper, the waiting time for the first appearance of an S-run of length k or an S∗-run of length r is systematically investigated. Exact formulae and Chen-Stein approximations are derived for the distribution of the waiting times in both linear and circular problems and their asymptotic behaviour is illustrated. Probability generating functions are also obtained when the trials are identical. Finally, practical applications of these results are discussed in some detail.
Stochastic scheduling for a two-machine open shop
Authors: Righter Rhonda
Published: July 2016

We study the problem of preemptive scheduling of jobs in a two-machine open shop. Jobs require processing on both machines, but the order does not matter. We define the D-LERPT (double longest expected remaining processing time) policy as the policy that first processes jobs that have not yet been processed by either machine (double jobs), in decreasing order of expected remaining processing times, and then processes jobs that require processing on only one machine in any order. We show that D-LERPT stochastically minimizes the makespan when preemption is not permitted and jobs (but not machines) are stochastically identical, and that D-LERPT minimizes the makespan in the increasing convex sense when preemption is permitted and the machines are stochastically identical and processing times are exponential or geometric with a job dependent rate.
A secretary problem with two decision makers
Authors: Chen Robert W. , Rosenberg Burton , Shepp Larry A.
Published: July 2016

n applicants of similar qualification are on an interview list and their salary demands are from a known and continuous distribution. Two managers, I and II, will interview them one at a time. Right after each interview, manager I always has the first opportunity to decide to hire the applicant or not unless he has hired one already. If manager I decides not to hire the current applicant, then manager II can decide to hire the applicant or not unless he has hired one already. If both managers fail to hire the current applicant, they interview the next applicant, but both lose the chance of hiring the current applicant. If one of the managers does hire the current one, then they proceed with interviews until the other manager also hires an applicant. The interview process continues until both managers hire an applicant each. However, at the end of the process, each manager must have hired an applicant. In this paper, we first derive the optimal strategies for them so that the probability that the one he hired demands less salary than the one hired by the other does is maximized. Then we derive an algorithm for computing manager II's winning probability when both managers play optimally. Finally, we show that manager II's winning probability is strictly increasing in n, is always less than c, and converges to c as n →∞, where c = 0.3275624139 · ·· is a solution of the equation ln(2) + x ln(x) = x.
Limit theorems for stochastically perturbed dynamical systems
Authors: Łoskot Krzysztof , Rudnicki Ryszard
Published: July 2016

We consider a discrete-time stochastically perturbed dynamical system on the Polish space given by the recurrence formulaXn=S(Xn–1,Yn),whereYnare i.i.d. random elements. We prove the existence of unique stationary measure and versions of classical limit theorems for the process (Xn).
Large exceedences for uniformly recurrent Markov-additive processes and strong-mixing stationary processes
Authors: Zajic Tim
Published: July 2016

We extend large exceedence results for i.i.d. -valued random variables to a class of uniformly recurrent Markov-additive processes and stationary strong-mixing processes. As in the i.i.d. case, the results are proved via large deviations estimates.
Limit theorems for the number of occurrences of consecutive k successes in n Markovian trials
Authors: Wang Y. H. , Ji Shuixin
Published: July 2016

We present a method of deriving the limiting distributions of the number of occurrences of success (S) runs of length k for all types of runs under the Markovian structure with stationary transition probabilities. In particular, we consider the following four bestknown types. 1. A string of S of exact length k preceded and followed by an F, except the first run which may not be preceded by an F, or the last run which may not be followed by an F. 2. A string of S of length k or more. 3. A string of S of exact length k, where recounting starts immediately after a run occurs. 4. A string of S of exact length k, allowing overlapping runs. It is shown that the limits are convolutions of two or more distributions with one of them being either Poisson or compound Poisson, depending on the type of runs in question. The completely stationary Markov case and the i.i.d. case are also treated.
Weak convergence of conditioned processes on a countable state space
Authors: Jacka S. D. , Roberts G. O.
Published: July 2016

We consider the problem of conditioning a continuous-time Markov chain (on a countably infinite state space) not to hit an absorbing barrier before time T; and the weak convergence of this conditional process as T → ∞. We prove a characterization of convergence in terms of the distribution of the process at some arbitrary positive time, t, introduce a decay parameter for the time to absorption, give an example where weak convergence fails, and give sufficient conditions for weak convergence in terms of the existence of a quasi-stationary limit, and a recurrence property of the original process.
Random walks in a quarter plane with zero drifts: transience and recurrence
Authors: Asymont I. M. , Fayolle G. , Menshikov Μ. V.
Published: July 2016

In this paper we continue the study of the classification problem for random walks in the quarter plane, with zero drifts in the interior of the domain. The necessary and sufficient conditions for these random walks to be ergodic were found earlier in [3]. Here we obtain necessary and sufficient conditions for transience by constructing suitable Lyapounov functions.
Distributions and expectations of singular random variables
Authors: Campbell L. L. , McKellips A. L. , Wittke P. H.
Published: July 2016

Intersymbol and cochannel interference in a communications channel can often be modelled as the sum of an infinite series of random variables with weights which decay fairly rapidly. Frequently, this yields a random variable which is singular but non-atomic. The Hausdorff dimension of the distribution is estimated and methods for calculating expectations are studied. A connection is observed between the dimension and the complexity of the calculation of an expectation.
Birth and death on a Brownian flow: a Feller semigroup and its generator and a martingale problem
Authors: Phelan Michael J.
Published: July 2016

We consider a system of particles in birth and death on a stochastic flow. The system includes a particle process tracking the spatial configuration of live particles on the flow. The particle process is a Markov process on the space of bounded counting measures. We show that its transition semigroup is a Feller semigroup and exhibit its pregenerator. The pregenerator defines a martingale problem. We show that the particle process solves the problem uniquely.
A spatial stochastic model of inter-plant competition
Authors: Diggle Peter J.
Published: July 2016

A stochastic model for inter-plant competition in a single-species population is presented, in which the probability that a given plant will be eliminated is defined in terms of the sizes and relative spatial locations of rival plants. The properties of the model are then investigated and illustrations of particular cases given, with particular emphasis on the distribution of the sizes of surviving plants. Empirical comparisons are made between the properties of the model and some experimental results due to Ford (1975b). Some possible extensions to the basic model are suggested.
Estimation of transition probabilities in a multiparticle semi-Markov system
Authors: Burman David
Published: July 2016

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) ∼ λt
α, 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.
Algebraic characterization of infinite Markov chains where movement to the right is limited to one step
Authors: Samuel-Cahn Ester , Zamir Shmuel
Published: July 2016

We consider an infinite Markov chain with states E
0, E
1, …, such that E
1, E
2, … is not closed, and for i ≧ 1 movement to the right is limited by one step. Simple algebraic characterizations are given for persistency of all states, and, if E
0 is absorbing, simple expressions are given for the probabilities of staying forever among the transient states. Examples are furnished, and simple necessary conditions and sufficient conditions for the above characterizations are given.
Some multivariate generalizations of results in univariate stationary point processes
Authors: Berman Mark
Published: July 2016

Some relationships are derived between the asynchronous and partially synchronous counting and interval processes associated with a multivariate stationary point process. A few examples are given to illustrate some of these relationships.
Numerical approximations for compound geometric distributions with applications in queueing theory
Authors: Delbrouck L. E. N.
Published: July 2016

A two-step procedure is described to approximate first come first served delay distributions in M/G/1 and GI/G/1 systems. The procedure consists in formulating a coarse initial approximation for the distribution sought, and then correcting this approximation by means of a suitable integral transformation. Examples are displayed.
Stochastic growth models: bounds on critical values
Authors: Durrett R.
Published: July 2016

We give upper bounds on the critical values for oriented percolation and some interacting particle systems by computing their behavior on small finite sets.
Rare events in series of queues
Authors: Tsoucas Pantelis
Published: July 2016

In an ergodic network of K M/M/1 queues in series we consider the rare event that, as N increases, the total population in the network exceeds N during a busy period. By utilizing the contraction principle of large deviation theory, an action functional is obtained for this exit problem. The ensuing minimization is carried out for K = 2 and an indication is given for arbitrary K. It is shown that, asymptotically and for unequal service rates, the ‘most likely' path for this rare event is one where the arrival rate has been interchanged with the smallest service rate. The problem has been posed in Parekh and Walrand [7] in connection with importance sampling simulation methods for queueing networks. Its solution has previously been obtained only heuristically.
Networks of non-homogeneous M/G/∞ systems
Authors: Keilson J. , Servi L. D.
Published: July 2016

For a network ofG/∞ service facilities, the transient joint distribution of the facility populations is shown by new simple methods to have a simple Poisson product form with simple explicit formulas for the means. In the network it is assumed that: (a) each facility has an infinite number of servers; (b) the service time distributions are general; (c) external traffic is non-homogeneous in time; (d) arrivals have random or deterministic routes through the network possibly returning to the same facility more than once; (e) arrivals use the facilities on their route sequentially or in parallel (as in the case of a circuitswitched telecommunication network). The results have relevance to communication networks and manufacturing systems.