Additive subordination of multiparameter Markov processes
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912960878739456 |
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| author | D'Onofrio, Giuseppe Mutti, Alessandro Semeraro, Patrizia |
| author_facet | D'Onofrio, Giuseppe Mutti, Alessandro Semeraro, Patrizia |
| contents | In this work, we consider, in a general setting, multiparameter multidimensional Markov processes that are time-changed by an independent additive subordinator. By extending Phillips theorem, we show that the resulting process is a Feller evolution and we characterize its generator. We further derive its pseudo-differential representation and show that its symbol admits a Lévy-Khintchine representation. In the specific case of multiparameter Ornstein-Uhlenbeck processes, we obtain explicit expression of the symbol, along with the associated characteristic Lévy triplet. As an application, we consider a factor-based specification for the Ornstein-Uhlenbeck process subordinated by a Sato process. The constructive nature of this process is inspired by applications in finance. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_20863 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Additive subordination of multiparameter Markov processes D'Onofrio, Giuseppe Mutti, Alessandro Semeraro, Patrizia Probability 60G53, 60J35, 47D07 In this work, we consider, in a general setting, multiparameter multidimensional Markov processes that are time-changed by an independent additive subordinator. By extending Phillips theorem, we show that the resulting process is a Feller evolution and we characterize its generator. We further derive its pseudo-differential representation and show that its symbol admits a Lévy-Khintchine representation. In the specific case of multiparameter Ornstein-Uhlenbeck processes, we obtain explicit expression of the symbol, along with the associated characteristic Lévy triplet. As an application, we consider a factor-based specification for the Ornstein-Uhlenbeck process subordinated by a Sato process. The constructive nature of this process is inspired by applications in finance. |
| title | Additive subordination of multiparameter Markov processes |
| topic | Probability 60G53, 60J35, 47D07 |
| url | https://arxiv.org/abs/2507.20863 |