香蕉视频

Title: Continuous-state branching processes with competition: Duality and Reflection at Infinity

Abstract: Continuous-state branching processes with quadratic competition have been defined by A. Lambert in 2005. Heuristically, the dynamics of the process are those of a branching process in continuous time and continuous-state space but with an additional quadratic death term modelling competition. At a constant rate, two individuals are picked at random and one kills the other. We ask ourselves how the competition may regulate the growth of the population size when the branching mechanism is of the most general form. A duality relation with some generalized Feller diffusions will allow us to classify completely the boundaries zero and infinity. In particular, we will see that in some cases, it is possible to construct an extension of the minimal process with infinity regular reflecting. In this latter case, the process typically reaches infinity by performing infinitely many large jumps in a finite interval of time and is instantaneously pushed back in $[0,\infty)$ by the competition.