Sticky diffusions on star graphs : characterization and It{ô} formula
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866914101561655296 |
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| author | Berry, Jules Colantoni, Fausto |
| author_facet | Berry, Jules Colantoni, Fausto |
| contents | We investigate continuous diffusions on star graphs with sticky behavior at the vertex. These are Markov processes with continuous paths having a positive occupation time at the vertex. We characterize sticky diffusions as time-changed nonsticky diffusions by adapting the classical technique of It{ô} and McKean. We prove a form of It{ô} formula, also known as Freidlin-Sheu formula, for this type of process. As an intermediate step, we also obtain a stochastic differential equation satisfied by the radial component of the process. These results generalize those already known for sticky diffusions on a half-line and skew sticky diffusions on the real line. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_05441 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Sticky diffusions on star graphs : characterization and It{ô} formula Berry, Jules Colantoni, Fausto Probability We investigate continuous diffusions on star graphs with sticky behavior at the vertex. These are Markov processes with continuous paths having a positive occupation time at the vertex. We characterize sticky diffusions as time-changed nonsticky diffusions by adapting the classical technique of It{ô} and McKean. We prove a form of It{ô} formula, also known as Freidlin-Sheu formula, for this type of process. As an intermediate step, we also obtain a stochastic differential equation satisfied by the radial component of the process. These results generalize those already known for sticky diffusions on a half-line and skew sticky diffusions on the real line. |
| title | Sticky diffusions on star graphs : characterization and It{ô} formula |
| topic | Probability |
| url | https://arxiv.org/abs/2411.05441 |