Sandra Palau Calderon (University of Bath): Extinction properties and asymptotic behaviour of multi-type

SZTE, TTIK, Bolyai Intézet,  Sztochasztika szeminárium

Abstract. First, we will discuss how to construct multi-type continuous state branching processes. Under mild conditions, we will see that there exists a lead eigenvalue associated with the first-moment semigroup. The sign of this eigenvalue distinguishes between the cases where there is extinction and exponential growth. Finally, in the supercritical case, we will give the a.s. rate of growth and the convergence of the proportion of each type.