We are interested in a population model called continuous-state branching process with dependent immigration (CBDI-processes). The immigration rate of the model depends on the current population size via a function that can be non-Lipschitz. We give a construction of the process using a stochastic equation driven by Poisson point measures on some path spaces. This approach gives a direct construction of the sample path of the process with general branching and immigration mechanisms from those of the corresponding CB-process without immigration. By choosing the ingredients suitably, we can get either a new CB-process with different branching mechanism or a branching model with competition. We focus on the one-dimensional model, but the arguments carry over to the measure-valued setting. These kinds of constructions have been proved useful for the study of some financial problems.

**Date**: 6 June 2018, 12:00 (Wednesday, 7th week, Trinity 2018)**Venue**: Mathematical Institute

Woodstock Road OX2 6GGSee location on maps.ox**Details**: L4**Speaker**: Zenghu Li (Beijing Normal University)**Organising department**: Department of Statistics**Organisers**: Christina Goldschmidt (Department of Statistics, University of Oxford), James Martin (Department of Statistics, University of Oxford)**Part of**: Probability seminar**Booking required?**: Not required**Audience**: Public- Editor: Christina Goldschmidt