On Decomposition of the Last Passage Time of Diffusions
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866911925287256064 |
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| author | Egami, Masahiko Kevkhishvili, Rusudan |
| author_facet | Egami, Masahiko Kevkhishvili, Rusudan |
| contents | For a regular transient diffusion, we provide a decomposition of its last passage time to a certain state $α$. This is accomplished by transforming the original diffusion into two diffusions using the occupation time of the area above and below $α$. Based on these two processes, both having a reflecting boundary at $α$, we derive the decomposition formula of the Laplace transform of the last passage time explicitly in a simple form in terms of Green functions. This equation also leads to the Green function's decomposition formula. We demonstrate an application of these formulas to a diffusion with two-valued parameters. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_01321 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On Decomposition of the Last Passage Time of Diffusions Egami, Masahiko Kevkhishvili, Rusudan Probability 60J60 For a regular transient diffusion, we provide a decomposition of its last passage time to a certain state $α$. This is accomplished by transforming the original diffusion into two diffusions using the occupation time of the area above and below $α$. Based on these two processes, both having a reflecting boundary at $α$, we derive the decomposition formula of the Laplace transform of the last passage time explicitly in a simple form in terms of Green functions. This equation also leads to the Green function's decomposition formula. We demonstrate an application of these formulas to a diffusion with two-valued parameters. |
| title | On Decomposition of the Last Passage Time of Diffusions |
| topic | Probability 60J60 |
| url | https://arxiv.org/abs/2210.01321 |