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Pré-Publication, Document De Travail Année : 2022

Quasi-stationary behavior for an hybrid model of chemostat: the Crump-Young model

Résumé

The Crump-Young model consists of two fully coupled stochastic processes modeling the substrate and microorganisms dynamics in a chemostat. Substrate evolves following an ordinary differential equation whose coefficients depend of microorganisms number. Microorganisms are modeled though a pure jump process whose the jump rates depend on the substrate concentration. It goes to extinction almost-surely in the sense that microorganism population vanishes. In this work, we show that, conditionally on the non-extinction, its distribution converges exponentially fast to a quasi-stationary distribution. Due to the deterministic part, the dynamics of the Crump-Young model is highly degenerated. The proof is then original and consists of technical sharp estimates and new approaches for the quasi-stationary convergence.
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Dates et versions

hal-03660678 , version 1 (09-05-2022)
hal-03660678 , version 2 (26-01-2024)

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Citer

Bertrand Cloez, Coralie Fritsch. Quasi-stationary behavior for an hybrid model of chemostat: the Crump-Young model. 2022. ⟨hal-03660678v1⟩

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