Upper bounds for survival probability of the contact process

A precise description of the nontrivial upper invariant measure for λ>λc is still an open problem for the basic contact process, which is a self-dual, attractive, but nonreversible Markov process of an interacting particle system. By its self-duality, to identify the invariant measure is equivalent to determining the initial-state dependence of the survival probability of the process. A procedure to give rigorous upper bounds for the survival probability is presented based on a lemma given by Harris. Two new bounds are given, improving the simple branching-process bound. In the one-dimensional case, the present procedure can be viewed as a trial to make approximate measures by generalized Markov extensions.

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