El jueves 7 de junio a las 12:30 horas, en el aula C3A del Edificio Carlos Benítez en Badajoz, la profesora Maroussia Slavtchova-Bojkova de la Sofia University «St. Kl. Ohridski», Bulgaria impartirá la conferencia con título «Limit results on non-decomposable age-dependent branching processes with immigration» .
Resumen:
This talk is concerned with the theoretical study of a class of non–decomposable branching processes, in discrete and continuous time, with two types of immigration – in the state zero and another one of a renewal type. The multidimensional case is considered and asymptotic properties and limit theorems are established both in subcritical and supercritical cases. These results generalize both the results of the discrete theory and those for the one–dimensional continuous–time model. A probabilistic proof under week conditions of the convergence in probability of the subcritical age–dependent branching processes (LLN) allowing two different types of immigration, i.e. one type in the state zero and another one according to the i.i.d. times of an independent ergodic renewal process is presented. A strong law of large numbers (SLLN) and a central limit theorem (CLT) for the Bellman–Harris process with immigration at zero and immigration of renewal type (BHPIOR) processes is proved for age-dependent BHPIORs. Similar conclusions are obtained for their discrete–time counterparts (lifetime per individual equals one), well-known as Galton–Watson processes with immigration at zero and immigration of renewal type (GWPIOR). Our approach in the last case is based on the theory of regenerative processes, renewal theory and occupation measures and is quite different from those in earlier related work using analytic tools. The study of the BHPIOR generalizing the convergence in probability (LLN) for p-type (p > 1) ones completes this research.
