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On an irreducibility type condition for the ergodicity of nonconservative semigroups

Abstract : We propose a simple criterion, inspired from the irreducible aperiodic Markov chains, to derive the exponential convergence of general positive semigroups. When not checkable on the whole state space, it can be combined to the use of Lyapunov functions. It differs from the usual generalization of irreducibility and is based on the accessibility of the trajectories of the underlying dynamics. It allows to obtain new existence results of principal eigenelements, and their exponential attractiveness, for a nonlocal selection-mutation population dynamics model defined in a space-time varying environment.
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Submitted on : Friday, October 16, 2020 - 12:19:03 PM
Last modification on : Wednesday, September 28, 2022 - 3:12:49 PM

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Bertrand Cloez, Pierre Gabriel. On an irreducibility type condition for the ergodicity of nonconservative semigroups. Comptes Rendus. Mathématique, Académie des sciences (Paris), 2020, 358 (6), pp.733-742. ⟨10.5802/crmath.92⟩. ⟨hal-02291295v2⟩

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