A mini course on continuous-state branching processes

Por M González Velasco.- Entre los días 23 y 26 de septiembre de 2019 el Profesor Zenghu Li (Beijing Normal University) impartirá un mini curso sobre «Continuous-state branching processes» en el Departamento de Matemáticas, Facultad de Ciencias, de la Universidad de Extremadura, Badajoz. El mini curso será impartido en inglés y estructurado en cinco sesiones de 2 horas y media. A continuación se pueden encontrar algunos detalles sobre el Profesor Zenghu Li y el curso.

About the speaker: Professor Zenghu Li is the Head of School of Mathematical, Beijing Normal University. His research interests are Markov processes (Measure-valued processes, branching processes, stochastic differential equations, stochastic models in finance, etc). He has published a large number of papers in this field. Moreover he has supervised several doctoral theses and participated in a large number of international conferences.

Abstract: This course provides a brief introduction to continuous-state branching processes with or without immigration. The processes are constructed by taking rescaling limits of classical discrete-state branching models. We give quick developments of the martingale problems and stochastic equations of the continuous-state processes. The proofs here are more elementary than those appearing in the literature before. We have made them accessible without too much preliminary knowledge on branching processes and stochastic analysis. Using the stochastic equations, we give characterizations of the local and global maximal jumps of the processes. Under suitable conditions, their strong Feller property and exponential ergodicity are studied by a coupling method based on one of the stochastic equations.

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