Spatial birth and death processes as solutions of stochastic equations

Spatial birth and death processes are obtained as solutions of a sys- tem of stochastic equations. The processes are required to be locally nite, but may involve an innite population over the full (noncompact) type space. Con- ditions 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.

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