On the large-time behaviour of affine Volterra processes
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866915497588555776 |
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| author | Jacquier, Antoine Pannier, Alexandre Spiliopoulos, Konstantinos |
| author_facet | Jacquier, Antoine Pannier, Alexandre Spiliopoulos, Konstantinos |
| contents | We show the existence of a stationary measure for a class of multidimensional stochastic Volterra systems of affine type. These processes are in general not Markovian, a shortcoming which hinders their large-time analysis. We circumvent this issue by lifting the system to a measure-valued stochastic evolution equation introduced by Cuchiero and Teichmann~\cite{CT18}, whence we retrieve the Markov property. Leveraging on the associated generalised Feller property, we extend the Krylov-Bogoliubov theorem to this infinite-dimensional setting and thus establish an approach to the existence of invariant measures. We present concrete examples, including the rough Heston model from Mathematical Finance. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2204_05270 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On the large-time behaviour of affine Volterra processes Jacquier, Antoine Pannier, Alexandre Spiliopoulos, Konstantinos Probability 60F05 (Primary) 60G22, 60H15, 60J25 (Secondary) We show the existence of a stationary measure for a class of multidimensional stochastic Volterra systems of affine type. These processes are in general not Markovian, a shortcoming which hinders their large-time analysis. We circumvent this issue by lifting the system to a measure-valued stochastic evolution equation introduced by Cuchiero and Teichmann~\cite{CT18}, whence we retrieve the Markov property. Leveraging on the associated generalised Feller property, we extend the Krylov-Bogoliubov theorem to this infinite-dimensional setting and thus establish an approach to the existence of invariant measures. We present concrete examples, including the rough Heston model from Mathematical Finance. |
| title | On the large-time behaviour of affine Volterra processes |
| topic | Probability 60F05 (Primary) 60G22, 60H15, 60J25 (Secondary) |
| url | https://arxiv.org/abs/2204.05270 |