  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 (noncompact) 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.
