Evolution of states of an infinite fission-death system

The evolution of an infinite system of interacting point entities with traits $x\in \mathds{R}^d$ is studied. The elementary acts of the evolution are state-dependent death of an entity with rate that includes a competition term and independent fission in the course of which an entity gives birth to two new entities and simultaneously disappears. The states of the system are probability measures on the corresponding configuration space and the main result of the paper is the construction of the evolution $\mu_0\to \mu_t$, $t>0$, of states in the class of sub-Poissonian measures.