Decay property of a class of d-dimensional Markov processes
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914141511352320 |
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| author | Li, Yanyun |
| author_facet | Li, Yanyun |
| contents | In this paper, we consider the decay property of a special class of $d$-dimensional Markov processes, which can be viewed as a stopped network with the external customer being blocked to empty nodes. The exact value of the decay parameter $λ_{\mathcal{C}}$ is obtained by using a new method. It is proved that the process is $λ_{\mathcal{C}}$-transient. The corresponding $λ_{\mathcal{C}}$-invariant measures and quasi-distributions are also presented. Finally, an example on auto quick repair service network is presented to illustrate the results obtained in this paper. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_18044 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Decay property of a class of d-dimensional Markov processes Li, Yanyun Probability In this paper, we consider the decay property of a special class of $d$-dimensional Markov processes, which can be viewed as a stopped network with the external customer being blocked to empty nodes. The exact value of the decay parameter $λ_{\mathcal{C}}$ is obtained by using a new method. It is proved that the process is $λ_{\mathcal{C}}$-transient. The corresponding $λ_{\mathcal{C}}$-invariant measures and quasi-distributions are also presented. Finally, an example on auto quick repair service network is presented to illustrate the results obtained in this paper. |
| title | Decay property of a class of d-dimensional Markov processes |
| topic | Probability |
| url | https://arxiv.org/abs/2404.18044 |