Rapid variation with remainder and rates of convergence

(op voorblad per abuis E. Beirland vermeld, in plaats van J. Beirlant) The remainder term of the class \Gamma$ of rapidly varying fuctions Is considered. Some probabilistic applIcations to limit laws of extreme value theory and to the estlmation of the indexparameter of a regularly varying tail are considered. Keywords and Phrases: regular variation, rates of convergence, domains of attraction

Migration and Settlement: A Multiregional Comparative Study

In 1976, the International Institute for Applied Systems Analysis initiated a study of migration and population distribution patterns in its 17 member nations. In each country, the analysis was carried out by a national scholar using techniques of multiregional demography. This paper describes the organization of the study, discusses the data bases used, evaluates the main results obtained, and reviews some of the methodological research that has been generated by the study. Among the conclusions of the paper are recommendations for researchers wishing to carry out a multiregional demographic analysis

Monitoring international migration flows in Europe. Towards a statistical data base combining data from different sources

The paper reviews techniques developed in demography, geography and statistics that are useful for bridging the gap between available data on international migration flows and the information required for policy making and research. The basic idea of the paper is as follows: to establish a coherent and consistent data base that contains sufficiently detailed, up-to-date and accurate information, data from several sources should be combined. That raises issues of definition and measurement, and of how to combine data from different origins properly. The issues may be tackled more easily if the statistics that are being compiled are viewed as different outcomes or manifestations of underlying stochastic processes governing migration. The link between the processes and their outcomes is described by models, the parameters of which must be estimated from the available data. That may be done within the context of socio-demographic accounting. The paper discusses the experience of the U.S. Bureau of the Census in combining migration data from several sources. It also summarizes the many efforts in Europe to establish a coherent and consistent data base on international migration. The paper was written at IIASA. It is part of the Migration Estimation Study, which is a collaborative IIASA-University of Groningen project, funded by the Netherlands Organization for Scientific Research (NWO). The project aims at developing techniques to obtain improved estimates of international migration flows by country of origin and country of destination

Comparing migration in Britain and Australia: Harmonisation through use of age-time plans

Differences in the way migration is measured impede cross-national comparisons of internal migration. In this paper we utilise age-time diagrams to elucidate these problems for Australia and the United Kingdom and present solutions which generate time series of interregional migration for the two countries, harmonised with respect to age-time plans. We achieve this through estimation of the numbers of migration transitions (Australia) or migration events (Britain) for common age-period-cohort (APC) spaces. We derive appropriate population stocks for computation of transition probabilities or occurrence-exposure rates. In the final section of the paper we present a series of migration-intensity calculations based on varying combinations of period-cohort, period-age, and age-period-cohort perspectives, to demonstrate the significance of the variations, and the errors that can arise without harmonisation

Convergence of the all-time supremum of a L\'evy process in the heavy-traffic regime

In this paper we derive a technique of obtaining limit theorems for suprema of L\'evy processes from their random walk counterparts. For each $a>0$, let $\{Y^{(a)}_n:n\ge 1\}$ be a sequence of independent and identically distributed random variables and $\{X^{(a)}_t:t\ge 0\}$ be a L\'evy processes such that $X_1^{(a)}\stackrel{d}{=} Y_1^{(a)}$, $\mathbb E X_1^{(a)}<0$ and $\mathbb E X_1^{(a)}\uparrow0$ as $a\downarrow0$. Let $S^{(a)}_n=\sum_{k=1}^n Y^{(a)}_k$. Then, under some mild assumptions, $\Delta(a)\max_{n\ge 0} S_n^{(a)}\stackrel{d}{\to} R\iff\Delta(a)\sup_{t\ge 0} X^{(a)}_t\stackrel{d}{\to} R$, for some random variable $R$ and some function $\Delta(\cdot)$. We utilize this result to present a number of limit theorems for suprema of L\'evy processes in the heavy-traffic regime