Fast exact simulation of the first passage of a tempered stable subordinator across a non-increasing function
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| Format: | Preprint |
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2023
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| _version_ | 1866910489323241472 |
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| author | Cázares, Jorge Ignacio González Lin, Feng Mijatović, Aleksandar |
| author_facet | Cázares, Jorge Ignacio González Lin, Feng Mijatović, Aleksandar |
| contents | We construct a fast exact algorithm for the simulation of the first-passage time, jointly with the undershoot and overshoot, of a tempered stable subordinator over an arbitrary non-increasing absolutely continuous function. We prove that the running time of our algorithm has finite exponential moments and provide bounds on its expected running time with explicit dependence on the characteristics of the process and the initial value of the function. The expected running time grows at most cubically in the stability parameter (as it approaches either $0$ or $1$) and is linear in the tempering parameter and the initial value of the function. Numerical performance, based on the implementation in the dedicated GitHub repository, exhibits a good agreement with our theoretical bounds. We provide numerical examples to illustrate the performance of our algorithm in Monte Carlo estimation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_11964 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Fast exact simulation of the first passage of a tempered stable subordinator across a non-increasing function Cázares, Jorge Ignacio González Lin, Feng Mijatović, Aleksandar Probability Numerical Analysis 60G51, 65C05 (Primary) 62E15, 60E07 (Secondary) We construct a fast exact algorithm for the simulation of the first-passage time, jointly with the undershoot and overshoot, of a tempered stable subordinator over an arbitrary non-increasing absolutely continuous function. We prove that the running time of our algorithm has finite exponential moments and provide bounds on its expected running time with explicit dependence on the characteristics of the process and the initial value of the function. The expected running time grows at most cubically in the stability parameter (as it approaches either $0$ or $1$) and is linear in the tempering parameter and the initial value of the function. Numerical performance, based on the implementation in the dedicated GitHub repository, exhibits a good agreement with our theoretical bounds. We provide numerical examples to illustrate the performance of our algorithm in Monte Carlo estimation. |
| title | Fast exact simulation of the first passage of a tempered stable subordinator across a non-increasing function |
| topic | Probability Numerical Analysis 60G51, 65C05 (Primary) 62E15, 60E07 (Secondary) |
| url | https://arxiv.org/abs/2303.11964 |