Some Probabilistic Results in a Bisexual Branching Process with Immigration

2000 Mathematics Subject Classification: 60J80.

Del este de Europa, al sur de América : migraciones soviéticas y post soviéticas a la ciudad de Bucaramanga, Santander

En este trabajo examinamos la migración de ciudadanos de la Ex-Unión Soviética a la ciudad de Bucaramanga. Migración que a pesar de su alto impacto regional no aparece en los registros estadísticos ni académicos. A través de las historias de vida reconstruimos los procesos migratorios de los migrantes, desde el momento en que deciden dejar sus regiones de origen, hasta su integración en la ciudad. Es un caso de estudio basado en varias teorias sobre la migración.

O setor de venture capital, as startups e o empreendedorismo em Israel, nos anos recentes

Some of the factors that help to explain the Israeli success case on promoting high-tech start-ups backed by venture capital funds can be found in the risk-taking culture of the country, the vast technological know-how associated with the huge military development, the high offer of human intellectual capital due to the immigration processes, and finally also the FDI inflows, mainly from the United States. Even though, these factors would not have the same effects in the economy unless the right structures were founded by the public-private sectors partnerships for the high-tech industry development and the adaptation of the investment industry surpasses two of the deepest global financial crisis: the dot-com bubble in the 2000’s and the subprime in 2008

Evaluating the legacy of landscape history: extinction debt and species credit in bird and small mammal assemblages in the Brazilian Atlantic Forest

There is now an extensive literature on extinction debt following deforestation. However, the potential for species credit in landscapes that have experienced a change from decreasing to expanding forest cover has received little attention. Both delayed responses should depend on current landscape forest cover and on species life-history traits, such as longevity, as short-lived species are likely to respond faster than long-lived species. We evaluated the effects of historical and present-day local forest cover on two vertebrate groups with different longevities understorey birds and non-flying small mammals - in forest patches at three Atlantic Forest landscapes. Our work investigated how the probability of extinction debt and species credit varies (i) amongst landscapes with different proportions of forest cover and distinct trajectories of forest cover change, and (ii) between taxa with different life spans. Our results suggest that the existence of extinction debt and species credit, as well as the potential for their future payment and/or receipt, is not only related to forest cover trajectory but also to the amount of remaining forest cover at the landscape scale. Moreover, differences in bird and small mammal life spans seem to be insufficient to affect differently their probability of showing time-delayed responses to landscape change. Synthesis and applications. Our work highlights the need for considering not only the trajectory of deforestation/regeneration but also the amount of forest cover at landscape scale when investigating time-delayed responses to landscape change. As many landscapes are experiencing a change from decreasing to expanding forest cover, understanding the association of extinction and immigration processes, as well as their interactions with the landscape dynamic, is a key factor to plan conservation and restoration actions in human-altered landscapes.

Birth-death processes with mass annihilation and state-dependent immigration

A birth-death process is subject to mass annihilation at rate β with subsequent mass immigration occurring into state j at rateα j . This structure enables the process to jump from one sector of state space to another one (via state 0) with transition rate independent of population size. First, we highlight the difficulties encountered when using standard techniques to construct both time-dependent and equilibrium probabilities. Then we show how to overcome such analytic difficulties by means of a tool developed in Chen and Renshaw (1990, 1993b); this approach is applicable to many processes whose underlying generator on E\{0} has known probability structure. Here we demonstrate the technique through application to the linear birth-death generator on which is superimposed an annihilation/immigration process.

Existence, recurrence and equilibrium properties of Markov branching processes with instantaneous immigration

Attention has recently focussed on stochastic population processes that can undergo total annihilation followed by immigration into state j at rate αj. The investigation of such models, called Markov branching processes with instantaneous immigration (MBPII), involves the study of existence and recurrence properties. However, results developed to date are generally opaque, and so the primary motivation of this paper is to construct conditions that are far easier to apply in practice. These turn out to be identical to the conditions for positive recurrence, which are very easy to check. We obtain, as a consequence, the surprising result that any MBPII that exists is ergodic, and so must possess an equilibrium distribution. These results are then extended to more general MBPII, and we show how to construct the associated equilibrium distributions.

Ergodicity and regularity of invariant measure for branching Markov processes with immigration

In this thesis we consider systems of finitely many particles moving on paths given by a strong Markov process and undergoing branching and reproduction at random times. The branching rate of a particle, its number of offspring and their spatial distribution are allowed to depend on the particle's position and possibly on the configuration of coexisting particles. In addition there is immigration of new particles, with the rate of immigration and the distribution of immigrants possibly depending on the configuration of pre-existing particles as well. In the first two chapters of this work, we concentrate on the case that the joint motion of particles is governed by a diffusion with interacting components. The resulting process of particle configurations was studied by E. Löcherbach (2002, 2004) and is known as a branching diffusion with immigration (BDI). Chapter 1 contains a detailed introduction of the basic model assumptions, in particular an assumption of ergodicity which guarantees that the BDI process is positive Harris recurrent with finite invariant measure on the configuration space. This object and a closely related quantity, namely the invariant occupation measure on the single-particle space, are investigated in Chapter 2 where we study the problem of the existence of Lebesgue-densities with nice regularity properties. For example, it turns out that the existence of a continuous density for the invariant measure depends on the mechanism by which newborn particles are distributed in space, namely whether branching particles reproduce at their death position or their offspring are distributed according to an absolutely continuous transition kernel. In Chapter 3, we assume that the quantities defining the model depend only on the spatial position but not on the configuration of coexisting particles. In this framework (which was considered by Höpfner and Löcherbach (2005) in the special case that branching particles reproduce at their death position), the particle motions are independent, and we can allow for more general Markov processes instead of diffusions. The resulting configuration process is a branching Markov process in the sense introduced by Ikeda, Nagasawa and Watanabe (1968), complemented by an immigration mechanism. Generalizing results obtained by Höpfner and Löcherbach (2005), we give sufficient conditions for ergodicity in the sense of positive recurrence of the configuration process and finiteness of the invariant occupation measure in the case of general particle motions and offspring distributions.

Branching Processes with Immigration and Integer-valued Time Series

In this paper, we indicate how integer-valued autoregressive time series Ginar(d) of ordre d, d ≥ 1, are simple functionals of multitype branching processes with immigration. This allows the derivation of a simple criteria for the existence of a stationary distribution of the time series, thus proving and extending some results by Al-Osh and Alzaid [1], Du and Li [9] and Gauthier and Latour [11]. One can then transfer results on estimation in subcritical multitype branching processes to stationary Ginar(d) and get consistency and asymptotic normality for the corresponding estimators. The technique covers autoregressive moving average time series as well.

A Limit Theorem for Multi-Type Subcritical Age-Dependent Branching Processes with two Types of Immigration

Марусия Н. Славчова-Божкова - В настоящата работа се обобщава една гранична теорема за докритичен многомерен разклоняващ се процес, зависещ от възрастта на частиците с два типа имиграция. Целта е да се обобщи аналогичен резултат в едномерния случай като се прилагат “coupling” метода, теория на възстановяването и регенериращи процеси.

Estimation of the Offspring and Immigration Mean Vectors for Bisexual Branching Processes with Immigration of Females and Males

2000 Mathematics Subject Classification: 60J80, 62M05.

Two-Type Age-Dependent Branching Processes with Inhomogeneous Immigration as Models of Renewing Cell Population

2000 Mathematics Subject Classification: primary 60J80; secondary 60J85, 92C37.

Offspring Mean Estimators in Branching Processes with Immigration

2000 Mathematics Subject Classification: 60J80.

Estimators in Branching Processes with Immigration

2000 Mathematics Subject Classi cation: 60J80.

A Computational Approach for the Statistical Estimation of Discrete Time Branching Processes with Immigration

2010 Mathematics Subject Classification: 60J80.