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Article Dans Une Revue Comptes Rendus. Mathématique Année : 2020

On an irreducibility type condition for the ergodicity of nonconservative semigroups

Résumé

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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Dates et versions

hal-02291295 , version 1 (18-09-2019)
hal-02291295 , version 2 (16-10-2020)

Identifiants

Citer

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