The Kolmogorov forward equation for a distributed model of regime-switching diffusions
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866918393077039104 |
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| author | Bratus, Alexander S. Rozanova, Olga S. |
| author_facet | Bratus, Alexander S. Rozanova, Olga S. |
| contents | For the regime-switching diffusion process with and without advection term we propose an integro-differential equation describing the densities of states continuously distributed over a segment. We demonstrate that there exists a constructive algorithm for solving the Cauchy problem. We then show that for some initial distributions of states, the solution can be found explicitly. We also discuss how a model with a discrete number of hidden states can be approximated by a model with continuously distributed states. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_21659 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Kolmogorov forward equation for a distributed model of regime-switching diffusions Bratus, Alexander S. Rozanova, Olga S. Analysis of PDEs 60E05, 35Q84, 35K57 For the regime-switching diffusion process with and without advection term we propose an integro-differential equation describing the densities of states continuously distributed over a segment. We demonstrate that there exists a constructive algorithm for solving the Cauchy problem. We then show that for some initial distributions of states, the solution can be found explicitly. We also discuss how a model with a discrete number of hidden states can be approximated by a model with continuously distributed states. |
| title | The Kolmogorov forward equation for a distributed model of regime-switching diffusions |
| topic | Analysis of PDEs 60E05, 35Q84, 35K57 |
| url | https://arxiv.org/abs/2601.21659 |