Functional convergence to the local time of a sticky diffusion
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866917829919375360 |
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| author | Anagnostakis, Alexis |
| author_facet | Anagnostakis, Alexis |
| contents | We establish the consistency of a local time approximation of a diffusion at a sticky threshold based on high-frequency observations. First, we prove the result for sticky Brownian motion, and then extend it to Itô diffusions with a sticky point (SID). For this, we derive the pathwise formulation of an SID along with respective versions of key stochastic calculus results (Itô formula, Girsanov theorem). Based on the local time approximation, we develop a consistent estimator for the stickiness parameter. We conclude with numerical experiments and assess statistical properties of the stickiness estimator and the local time approximation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2202_03698 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Functional convergence to the local time of a sticky diffusion Anagnostakis, Alexis Probability 60F17, 60J55, 60J60 We establish the consistency of a local time approximation of a diffusion at a sticky threshold based on high-frequency observations. First, we prove the result for sticky Brownian motion, and then extend it to Itô diffusions with a sticky point (SID). For this, we derive the pathwise formulation of an SID along with respective versions of key stochastic calculus results (Itô formula, Girsanov theorem). Based on the local time approximation, we develop a consistent estimator for the stickiness parameter. We conclude with numerical experiments and assess statistical properties of the stickiness estimator and the local time approximation. |
| title | Functional convergence to the local time of a sticky diffusion |
| topic | Probability 60F17, 60J55, 60J60 |
| url | https://arxiv.org/abs/2202.03698 |