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            <title xml:lang="en">Catalytic branching processes via spine techniques and renewal theory</title>
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              <p>In this article we contribute to the moment analysis of branching processes in catalytic media. The many-to-few lemma based on the spine technique is used to derive a system of (discrete space) partial differential equations for the number of particles in a variation of constants formulation. The long-time behavior is then deduced from renewal theorems and induction.</p>
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