Approximation and estimation of scale functions for spectrally negative Levy processes
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916450002796544 |
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| author | Irie, Haruka Shimizu, Yasutaka |
| author_facet | Irie, Haruka Shimizu, Yasutaka |
| contents | The scale function holds significant importance within the fluctuation theory of Levy processes, particularly in addressing exit problems. However, its definition is established through the Laplace transform, thereby lacking explicit representations in general. This paper introduces a novel series representation for this scale function, employing Laguerre polynomials to construct a uniformly convergent approximate sequence. Additionally, we derive statistical inference based on specific discrete observations, presenting estimators of scale functions that are asymptotically normal. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_13599 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Approximation and estimation of scale functions for spectrally negative Levy processes Irie, Haruka Shimizu, Yasutaka Statistics Theory 60G51, 62M86, 62P05 The scale function holds significant importance within the fluctuation theory of Levy processes, particularly in addressing exit problems. However, its definition is established through the Laplace transform, thereby lacking explicit representations in general. This paper introduces a novel series representation for this scale function, employing Laguerre polynomials to construct a uniformly convergent approximate sequence. Additionally, we derive statistical inference based on specific discrete observations, presenting estimators of scale functions that are asymptotically normal. |
| title | Approximation and estimation of scale functions for spectrally negative Levy processes |
| topic | Statistics Theory 60G51, 62M86, 62P05 |
| url | https://arxiv.org/abs/2402.13599 |