Regularity of models associated with Markov jump processes
We consider a jump Markov process X=(Xt)t≥0X={\left({X}_{t})}_{t\ge 0}, with values in a state space (E,ℰ)\left(E,{\mathcal{ {\mathcal E} }}). We suppose that the corresponding infinitesimal generator πθ(x,dy),x∈E{\pi }_{\theta }\left(x,{\rm{d}}y),x\in E, hence the law Px,θ{{\mathbb{P}}}_{x,\theta }...
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| Format: | Article |
| Language: | English |
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De Gruyter
2022-09-01
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| Series: | Open Mathematics |
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| Online Access: | https://doi.org/10.1515/math-2022-0482 |
| _version_ | 1797998356503461888 |
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| author | Jedidi Wissem |
| author_facet | Jedidi Wissem |
| author_sort | Jedidi Wissem |
| collection | DOAJ |
| description | We consider a jump Markov process X=(Xt)t≥0X={\left({X}_{t})}_{t\ge 0}, with values in a state space (E,ℰ)\left(E,{\mathcal{ {\mathcal E} }}). We suppose that the corresponding infinitesimal generator πθ(x,dy),x∈E{\pi }_{\theta }\left(x,{\rm{d}}y),x\in E, hence the law Px,θ{{\mathbb{P}}}_{x,\theta } of XX, depends on a parameter θ∈Θ\theta \in \Theta . We prove that several models (filtered or not) associated with XX are linked, by their regularity according to a certain scheme. In particular, we show that the regularity of the model (πθ(x,dy))θ∈Θ{\left({\pi }_{\theta }\left(x,{\rm{d}}y))}_{\theta \in \Theta } is equivalent to the local regularity of (Px,θ)θ∈Θ{\left({{\mathbb{P}}}_{x,\theta })}_{\theta \in \Theta }. |
| first_indexed | 2024-04-11T10:47:24Z |
| format | Article |
| id | doaj.art-2ec22ca7bb3c42b3aa2a5ef860ac75a9 |
| institution | Directory Open Access Journal |
| issn | 2391-5455 |
| language | English |
| last_indexed | 2024-04-11T10:47:24Z |
| publishDate | 2022-09-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Open Mathematics |
| spelling | doaj.art-2ec22ca7bb3c42b3aa2a5ef860ac75a92022-12-22T04:29:00ZengDe GruyterOpen Mathematics2391-54552022-09-0120191193010.1515/math-2022-0482Regularity of models associated with Markov jump processesJedidi Wissem0Department of Statistics & OR, King Saud University, College of Sciences, Riyadh 11451, Kingdom of Saudi ArabiaWe consider a jump Markov process X=(Xt)t≥0X={\left({X}_{t})}_{t\ge 0}, with values in a state space (E,ℰ)\left(E,{\mathcal{ {\mathcal E} }}). We suppose that the corresponding infinitesimal generator πθ(x,dy),x∈E{\pi }_{\theta }\left(x,{\rm{d}}y),x\in E, hence the law Px,θ{{\mathbb{P}}}_{x,\theta } of XX, depends on a parameter θ∈Θ\theta \in \Theta . We prove that several models (filtered or not) associated with XX are linked, by their regularity according to a certain scheme. In particular, we show that the regularity of the model (πθ(x,dy))θ∈Θ{\left({\pi }_{\theta }\left(x,{\rm{d}}y))}_{\theta \in \Theta } is equivalent to the local regularity of (Px,θ)θ∈Θ{\left({{\mathbb{P}}}_{x,\theta })}_{\theta \in \Theta }.https://doi.org/10.1515/math-2022-0482fisher information matrixhellinger integralsinfinitesimal generatorisomorphismjump markov processlikelihood processeslocal regularityrandomizationregularity of models65c2062m20 |
| spellingShingle | Jedidi Wissem Regularity of models associated with Markov jump processes Open Mathematics fisher information matrix hellinger integrals infinitesimal generator isomorphism jump markov process likelihood processes local regularity randomization regularity of models 65c20 62m20 |
| title | Regularity of models associated with Markov jump processes |
| title_full | Regularity of models associated with Markov jump processes |
| title_fullStr | Regularity of models associated with Markov jump processes |
| title_full_unstemmed | Regularity of models associated with Markov jump processes |
| title_short | Regularity of models associated with Markov jump processes |
| title_sort | regularity of models associated with markov jump processes |
| topic | fisher information matrix hellinger integrals infinitesimal generator isomorphism jump markov process likelihood processes local regularity randomization regularity of models 65c20 62m20 |
| url | https://doi.org/10.1515/math-2022-0482 |
| work_keys_str_mv | AT jedidiwissem regularityofmodelsassociatedwithmarkovjumpprocesses |