Age-structured stochastic populations under dynamic harvesters' behavior: well-posedness, asymptotic stability and numerically-amenable approximations
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866911178667589632 |
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| author | Ávila-Thieme, M. Isidora Martínez, Kerlyns Olivero, Héctor Tejo, Mauricio Videla, Leonardo |
| author_facet | Ávila-Thieme, M. Isidora Martínez, Kerlyns Olivero, Héctor Tejo, Mauricio Videla, Leonardo |
| contents | In this paper we study a model of age-structured ecological populations in continuous interaction with a community of harvesters. We propose an individual-based model for this feedback interactions and prove its convergence to a system of coupled stochastic differential equations. This limit process is complemented with socio-ecological and environmental factors.
For the resulting system we establish well-posedness, positivity, and the non-attainability of extinction boundaries, together with its long-term behavior and numerical approximation, relying on ad-hoc arguments to handle the super-linear growth and non-Lipschitz coefficients. Finally, we illustrate some of our findings with numerical experiments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_22513 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Age-structured stochastic populations under dynamic harvesters' behavior: well-posedness, asymptotic stability and numerically-amenable approximations Ávila-Thieme, M. Isidora Martínez, Kerlyns Olivero, Héctor Tejo, Mauricio Videla, Leonardo Probability 92-10, 65C30 In this paper we study a model of age-structured ecological populations in continuous interaction with a community of harvesters. We propose an individual-based model for this feedback interactions and prove its convergence to a system of coupled stochastic differential equations. This limit process is complemented with socio-ecological and environmental factors. For the resulting system we establish well-posedness, positivity, and the non-attainability of extinction boundaries, together with its long-term behavior and numerical approximation, relying on ad-hoc arguments to handle the super-linear growth and non-Lipschitz coefficients. Finally, we illustrate some of our findings with numerical experiments. |
| title | Age-structured stochastic populations under dynamic harvesters' behavior: well-posedness, asymptotic stability and numerically-amenable approximations |
| topic | Probability 92-10, 65C30 |
| url | https://arxiv.org/abs/2509.22513 |