On Approximation of Some Lévy Processes
In this paper, we extend the Asmussen-Rosinski approach for the approximation of Levy processes. To simulate the value of the process at time t, we introduce a time-dependent truncation of the Levy measure, which we refer to as dynamic cutting, followed by the simulation of the large-jump componen...
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| Format: | Article |
| Language: | English |
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Austrian Statistical Society
2025-01-01
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| Series: | Austrian Journal of Statistics |
| Online Access: | https://www.ajs.or.at/index.php/ajs/article/view/1991 |
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| author | Dmytro Ivanenko Victoria Knopova Denis Platonov |
| author_facet | Dmytro Ivanenko Victoria Knopova Denis Platonov |
| author_sort | Dmytro Ivanenko |
| collection | DOAJ |
| description |
In this paper, we extend the Asmussen-Rosinski approach for the approximation of Levy processes. To simulate the value of the process at time t, we introduce a time-dependent truncation of the Levy measure, which we refer to as dynamic cutting, followed by the simulation of the large-jump component. We provide the sufficient condition under which the compensated small-jump part can be replaced by a Gaussian approximation. We also derive weak approximation rates for both approaches. Finally, we run numerical simulations and compare the performance of our method with the Asmussen-Rosinski approach.
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| format | Article |
| id | doaj-art-bf87cddad4ef4ec4822808fca6a2fefd |
| institution | Kabale University |
| issn | 1026-597X |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Austrian Statistical Society |
| record_format | Article |
| series | Austrian Journal of Statistics |
| spelling | doaj-art-bf87cddad4ef4ec4822808fca6a2fefd2025-01-13T07:12:20ZengAustrian Statistical SocietyAustrian Journal of Statistics1026-597X2025-01-0154110.17713/ajs.v54i1.1991On Approximation of Some Lévy ProcessesDmytro IvanenkoVictoria Knopova0Denis PlatonovKyiv Taras Shevcjenko National University In this paper, we extend the Asmussen-Rosinski approach for the approximation of Levy processes. To simulate the value of the process at time t, we introduce a time-dependent truncation of the Levy measure, which we refer to as dynamic cutting, followed by the simulation of the large-jump component. We provide the sufficient condition under which the compensated small-jump part can be replaced by a Gaussian approximation. We also derive weak approximation rates for both approaches. Finally, we run numerical simulations and compare the performance of our method with the Asmussen-Rosinski approach. https://www.ajs.or.at/index.php/ajs/article/view/1991 |
| spellingShingle | Dmytro Ivanenko Victoria Knopova Denis Platonov On Approximation of Some Lévy Processes Austrian Journal of Statistics |
| title | On Approximation of Some Lévy Processes |
| title_full | On Approximation of Some Lévy Processes |
| title_fullStr | On Approximation of Some Lévy Processes |
| title_full_unstemmed | On Approximation of Some Lévy Processes |
| title_short | On Approximation of Some Lévy Processes |
| title_sort | on approximation of some levy processes |
| url | https://www.ajs.or.at/index.php/ajs/article/view/1991 |
| work_keys_str_mv | AT dmytroivanenko onapproximationofsomelevyprocesses AT victoriaknopova onapproximationofsomelevyprocesses AT denisplatonov onapproximationofsomelevyprocesses |