This study explores the impacts of the 2008–2009 economic crisis on joblessness in Turkey, incorporating into the analysis the marginally attached who would like to work if the opportunity existed, but are not actively searching for a job. We find that women were more likely than men to have a marginally attached status over the whole period of analysis, and during the time of the crisis, the number of marginally attached grew significantly faster for women than for men. The transition probability for the employed to become marginally attached and move out of the labour force rose substantially more for women than it did for men. The results obtained have important implications. Using conventional criteria, it is not possible to identify the degree of motivation to work or search for work in the case of women in Turkey, where the possibilities of shifting the care of burden to someone else or an institution are very limited, as a result of inadequate provisioning of public care services.

For the last 20 years, Galactic Surveys have been revolutionizing our vision of the universe and broadening our understanding of the vastness of space that surrounds us. Galactic Surveys such as APOGEE, Gaia-ESO, GALAH, WEAVE and the currently-under-development 4MOST are teaching us a great deal about the chemical composition of stellar atmospheres, the formation and evolution of galaxies and how elements are synthesised in the universe. However, many questions remain unanswered and the current focus of ongoing and future surveys. Answering each of these questions requires the collection of data, normally as spectra, as most of the information we receive from the universe is electromagnetic radiation. Following the very expensive acquisition of astronomical spectra, another crucial task lies ahead: the analysis of these spectra to extract the priceless information they carry. High-quality atomic data of many neutral and ionised species is essential to conduct this analysis.

This analysis examines aggregate structural changes in the United States dairy industry, 1987–2017. We estimate the likelihood of operation changes in herd size, entry, or exits for each of the lower 48 states using a semiparametric Markov process model. Small- and medium-sized dairy longevity correlates with higher dairy margins and productivity improvements. An increase in consumer expenditures on dairy products is associated with smaller operation exits. Industry dynamics exhibit a persistent trend toward consolidation in most states. The exit probability for each state and all size classes has increased significantly for most states since 2002.

Reliable spectroscopic data are needed for interpretation and modeling of observed astrophysical plasmas. For heavy element ions, which have complex spectra, experimental data are rather incomplete. To provide valuable fundamental quantities, such as precise wavelengths, level energies and semi-empirical transition probabilities, we are carrying out laboratory studies of high-resolution VUV emission spectra of moderately charged ions of transition metals and rare earth elements. Experimental and theoretical methods are summarized. Examples of studies are described.

Surveys of chronic health conditions provide information about prevalence but not incidence and the process of change within the population. Our study shows how “age dynamics” of chronic conditions – the probabilities of contracting conditions at different ages, of moving from one chronic condition state to another, and of dying – can be inferred from prevalence data for those conditions that can be viewed as irreversible. Transition probability matrices are constructed for successive age groups, with the sequence representing the age dynamics of the health conditions for a stationary population. We simulate the life path of a cohort under the initial probabilities, and again under altered probabilities, to explore the effects of reducing the incidence or mortality rate associated with a particular condition. We show that such surveys of chronic conditions can be made even more valuable by allowing the calculation of the transition probabilities that define the chronic conditions aging process

For a Markov two-dimensional death-process of a special class we consider the use of Fourier methods to obtain an exact solution of the Kolmogorov equations for the exponential (double) generating function of the transition probabilities. Using special functions, we obtain an integral representation for the generating function of the transition probabilities. We state the expression of the expectation and variance of the stochastic process and establish a limit theorem.

This paper is concerned with the development and operation of Continuing Care Retirement Communities (CCRCs). The paper examines the financial structure of a CCRC, being developed by the Joseph Rowntree Housing Trust, and describes a population model utilising transition probabilities to project care needs and financial performance.

The paper then explores the possibility of commercial organisations becoming involved in this market, and examines the risks that such a venture would entail and the strategies that may be adopted to reduce these risks.

In this paper we model the life-history of LTC-patients using a Markovian multi-state model in order to calculate premiums for a given LTC-plan. Instead of estimating the transition intensities in this model we use the approach suggested by Andersen et al. (2003) for a direct estimation of the transition probabilities. Based on the Aalen-Johansen estimator, an almost unbiased estimator for the transition matrix of a Markovian multi-state model, we calculate so-called pseudo-values, known from Jackknife methods. Further, we assume that the relationship between these pseudo-values and the covariates of our data are given by a GLM with the logit as link-function. Since the GLMs do not allow for correlation between successive observations we use instead the “Generalized Estimating Equations” (GEEs) to estimate the parameters of our regression model. The approach is illustrated using a representative sample from a German LTC portfolio.

For truncated birth-and-death processes with two absorbing or two reflecting boundaries, necessary and sufficient conditions on the transition rates are given such that the transition probabilities satisfy a suitable spatial symmetry relation. This allows one to obtain simple expressions for first-passage-time densities and for certain avoiding transition probabilities. An application to an M/M/1 queueing system with two finite sequential queueing rooms of equal sizes is finally provided.

This paper gives necessary and sufficient conditions for the convergence in distribution of sums of the 0–1 Markov chains to a compound Poisson distribution.

This paper is concerned with two problems in connection with exponential ergodicity for birth-death processes on a semi-infinite lattice of integers. The first is to determine from the birth and death rates whether exponential ergodicity prevails. We give some necessary and some sufficient conditions which suffice to settle the question for most processes encountered in practice. In particular, a complete solution is obtained for processes where, from some finite state n onwards, the birth and death rates are rational functions of n. The second, more difficult, problem is to evaluate the decay parameter of an exponentially ergodic birth-death process. Our contribution to the solution of this problem consists of a number of upper and lower bounds.

An ‘oscillating' version of Brownian motion is defined and studied. ‘Ordinary' Brownian motion and ‘reflecting' Brownian motion are shown to arise as special cases. Transition densities, first-passage time distributions, and occupation time distributions for the process are obtained explicitly. Convergence of a simple oscillating random walk to an oscillating Brownian motion process is established by using results of Stone (1963).

In this article we consider a generalisation of conservative processes in which the usual transition rate parameters are replaced by time-dependent stochastic variables. The main result of the article shows that these generalised processes which we call conservative processes with stochastic rates have transition probabilities which can be characterised in terms of exchangeable random variables in a manner similar to the characterisation of conservative processes in terms of independent random variables given by Bartlett (1949). We use this characterisation to obtain general expressions for the transition probabilities and to examine some limiting aspects of the processes. The carrier-borne epidemic is treated as a particular case of these generalised processes.

Recently, Billard (1973) derived a solution to the forward equations of the general stochastic model. This solution contains some recursively defined constants. In this paper we solve these forward equations along each of the paths the process can follow to absorption. A convenient method of combining the solutions for the different paths results in a simplified non-recursive expression for the transition probabilities of the process.

It is known [9] that geometric or exponential decay of a Markov chain is preserved under derivation (as defined by Cohen [2]). In this paper we consider the inverse problem, i.e., does a derived Markov chain with a geometrical or exponential decay necessarily arise from a Markov chain having the same property. For a large class of Markov chains (including time reversible chains) a complete solution is found. The method used in this paper proved accurate for obtaining exact results on the value of the decay parameter. An example extending results of Miller [8] and Teugels [9] illustrates the procedure.

This paper is concerned with a class of dynamic network flow problems in which the amount of flow leaving node i in one time period for node j is the fraction pij of the total amount of flow which arrived at node i during the previous time period. The fraction pij whose sum over j equals unity may be interpreted as the transition probability of a finite Markov chain in that the unit flow in state i will move to state j with probability pij during the next period of time. The conservation equations for this class of flows are derived, and the limiting behavior of the flows in the network as related to the properties of the fractions Pij are discussed.