Nancy L. Garcia (UNICAMP)
Spatial birth and death processes as solutions of stochastic equations

Spatial birth and death processes are obtained as solutions of a system of stochastic equations. The processes are required to be locally finite, but may involve an infinite population over the full (non-compact) type space. Conditions are given for existence and uniqueness of such solutions, and for temporal and spatial ergodicity. For birth and death processes with constant death rate, a sub-criticality condition on the birth rate implies that the process is ergodic and converges exponentially fast to the stationary distribution.