Investigation and Development of the Methodologies for Simulating Self-similar Processes
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866915660309725184 |
|---|---|
| author | Peng, Qidi Wu, William |
| author_facet | Peng, Qidi Wu, William |
| contents | This paper is devoted to the study of simulating a large class of self-similar processes. Since most current simulation approaches are limited to case-by-case studies, every existing approach has its constraints and flaws; hence a general and efficient simulation approach is in demand. Our study sheds some light in this direction. The paper's contributions are bi-fold. First, reviews and improvements are made to some existing methods for simulating specific self-similar processes. Second, we propose a novel method to simulate a general self-similar process, where we use a modified inverse Lamperti transformation to transform self-similarity to stationarity. Successful applications are made to simulate fractional Brownian motion and sub-fractional Brownian motion. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_07296 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Investigation and Development of the Methodologies for Simulating Self-similar Processes Peng, Qidi Wu, William Probability 60G18, 60G22, 60G10, 65C10 This paper is devoted to the study of simulating a large class of self-similar processes. Since most current simulation approaches are limited to case-by-case studies, every existing approach has its constraints and flaws; hence a general and efficient simulation approach is in demand. Our study sheds some light in this direction. The paper's contributions are bi-fold. First, reviews and improvements are made to some existing methods for simulating specific self-similar processes. Second, we propose a novel method to simulate a general self-similar process, where we use a modified inverse Lamperti transformation to transform self-similarity to stationarity. Successful applications are made to simulate fractional Brownian motion and sub-fractional Brownian motion. |
| title | Investigation and Development of the Methodologies for Simulating Self-similar Processes |
| topic | Probability 60G18, 60G22, 60G10, 65C10 |
| url | https://arxiv.org/abs/2512.07296 |