On the Cauchy problem for non-local Ornstein--Uhlenbeck operators
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2015
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| _version_ | 1866929334872178688 |
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| author | Priola, Enrico Tracà, Stefano |
| author_facet | Priola, Enrico Tracà, Stefano |
| contents | We study the Cauchy problem involving non-local Ornstein-Uhlenbeck operators in finite and infinite dimensions. We prove classical solvability without requiring that the Lévy measure corresponding to the large jumps part has a first finite moment. Moreover, we determine a core of regular functions which is invariant for the associated transition Markov semigroup. Such a core allows to characterize the marginal laws of the Ornstein-Uhlenbeck stochastic process as unique solutions to Fokker-Planck-Kolmogorov equations for measures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1505_01876 |
| institution | arXiv |
| publishDate | 2015 |
| record_format | arxiv |
| spellingShingle | On the Cauchy problem for non-local Ornstein--Uhlenbeck operators Priola, Enrico Tracà, Stefano Analysis of PDEs Probability 35K15, 60H10, 60J75, 47D07 We study the Cauchy problem involving non-local Ornstein-Uhlenbeck operators in finite and infinite dimensions. We prove classical solvability without requiring that the Lévy measure corresponding to the large jumps part has a first finite moment. Moreover, we determine a core of regular functions which is invariant for the associated transition Markov semigroup. Such a core allows to characterize the marginal laws of the Ornstein-Uhlenbeck stochastic process as unique solutions to Fokker-Planck-Kolmogorov equations for measures. |
| title | On the Cauchy problem for non-local Ornstein--Uhlenbeck operators |
| topic | Analysis of PDEs Probability 35K15, 60H10, 60J75, 47D07 |
| url | https://arxiv.org/abs/1505.01876 |