Survival of one dimensional renewal contact process
Fuente:
arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866916398123450368 |
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| author | Santos, Rafael Vares, Maria Eulalia |
| author_facet | Santos, Rafael Vares, Maria Eulalia |
| contents | The renewal contact process, introduced in $2019$ by Fontes, Marchetti, Mountford, and Vares, extends the Harris contact process in $\mathbb{Z}^d$ by allowing the possible cure times to be determined according to independent renewal processes (with some interarrival distribution $μ$) and keeping the transmission times determined according to independent exponential times with a fixed rate $λ$. We investigate sufficient conditions on $μ$ to have a process with a finite critical value $λ_c$ for any spatial dimension $d \geq 1$. In particular, we show that $λ_c$ is finite when $μ$ is continuous with bounded support or when $μ$ is absolutely continuous and has a decreasing hazard rate. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_06718 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Survival of one dimensional renewal contact process Santos, Rafael Vares, Maria Eulalia Probability 60K35, 60K05, 82B43 The renewal contact process, introduced in $2019$ by Fontes, Marchetti, Mountford, and Vares, extends the Harris contact process in $\mathbb{Z}^d$ by allowing the possible cure times to be determined according to independent renewal processes (with some interarrival distribution $μ$) and keeping the transmission times determined according to independent exponential times with a fixed rate $λ$. We investigate sufficient conditions on $μ$ to have a process with a finite critical value $λ_c$ for any spatial dimension $d \geq 1$. In particular, we show that $λ_c$ is finite when $μ$ is continuous with bounded support or when $μ$ is absolutely continuous and has a decreasing hazard rate. |
| title | Survival of one dimensional renewal contact process |
| topic | Probability 60K35, 60K05, 82B43 |
| url | https://arxiv.org/abs/2306.06718 |