On the exponential integrability of the derivative of intersection and self-intersection local time for Brownian motion and related processes
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866917633317666816 |
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| author | Das, Kaustav Markowsky, Greg Wu, Binghao |
| author_facet | Das, Kaustav Markowsky, Greg Wu, Binghao |
| contents | We show that the derivative of the intersection and self-intersection local times of alpha-stable processes are exponentially integrable for certain parameter values. This includes the Brownian motion case. We also discuss related results present in the literature for fractional Brownian motion, and in particular give a counter-example to a result in [Guo, J., Hu, Y., and Xiao, Y., Higher-order derivative of intersection local time for two independent fractional Brownian motions, Journal of Theoretical Probability 32, (2019), pp. 1190-1201] related to this question. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_05170 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the exponential integrability of the derivative of intersection and self-intersection local time for Brownian motion and related processes Das, Kaustav Markowsky, Greg Wu, Binghao Probability 60J55, 60J65, 60G52 We show that the derivative of the intersection and self-intersection local times of alpha-stable processes are exponentially integrable for certain parameter values. This includes the Brownian motion case. We also discuss related results present in the literature for fractional Brownian motion, and in particular give a counter-example to a result in [Guo, J., Hu, Y., and Xiao, Y., Higher-order derivative of intersection local time for two independent fractional Brownian motions, Journal of Theoretical Probability 32, (2019), pp. 1190-1201] related to this question. |
| title | On the exponential integrability of the derivative of intersection and self-intersection local time for Brownian motion and related processes |
| topic | Probability 60J55, 60J65, 60G52 |
| url | https://arxiv.org/abs/2404.05170 |