Invariant measures for contact processes with state-dependent birth and death rates

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Abstract

We consider contact processes on locally compact separable metric spaces with birth and death rates that are heterogeneous in space. We formulate conditions on the rates that ensure the existence of invariant measures of contact processes. One of the crucial conditions is the so-called critical regime condition. To prove the existence of invariant measures, we use the approach proposed in our preceding paper. We discuss in detail the multi-species contact model with a compact space of marks (species) in which both birth and death rates depend on the marks.

About the authors

E. A Zhizhina

Kharkevich Institute for Information Transmission Problems of the Russian Academy of Sciences

Email: ejj@iitp.ru
Moscow, Russia

S. A Pirogov

Kharkevich Institute for Information Transmission Problems of the Russian Academy of Sciences

Email: s.a.pirogov@bk.ru
Moscow, Russia

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