Strong solution and approximation of time-dependent radial Dunkl processes with multiplicative noise
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916438065807360 |
|---|---|
| author | Do, Minh-Thang Ngo, Hoang-Long Taguchi, Dai |
| author_facet | Do, Minh-Thang Ngo, Hoang-Long Taguchi, Dai |
| contents | We study the strong existence and uniqueness of solutions within a Weyl chamber for a class of time-dependent particle systems driven by multiplicative noise. This class includes well-known processes in physics and mathematical finance. We propose a method to prove the existence of negative moments for the solutions. This result allows us to analyze two numerical schemes for approximating the solutions. The first scheme is a $θ$-Euler--Maruyama scheme, which ensures that the approximated solution remains within the Weyl chamber. The second scheme is a truncated $θ$-Euler--Maruyama scheme, which produces values in $\mathbb{R}^{d}$ instead of the Weyl chamber $\mathbb{W}$, offering improved computational efficiency. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_10457 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Strong solution and approximation of time-dependent radial Dunkl processes with multiplicative noise Do, Minh-Thang Ngo, Hoang-Long Taguchi, Dai Probability Numerical Analysis 65C30, 60H35, 91G60, 17B22 We study the strong existence and uniqueness of solutions within a Weyl chamber for a class of time-dependent particle systems driven by multiplicative noise. This class includes well-known processes in physics and mathematical finance. We propose a method to prove the existence of negative moments for the solutions. This result allows us to analyze two numerical schemes for approximating the solutions. The first scheme is a $θ$-Euler--Maruyama scheme, which ensures that the approximated solution remains within the Weyl chamber. The second scheme is a truncated $θ$-Euler--Maruyama scheme, which produces values in $\mathbb{R}^{d}$ instead of the Weyl chamber $\mathbb{W}$, offering improved computational efficiency. |
| title | Strong solution and approximation of time-dependent radial Dunkl processes with multiplicative noise |
| topic | Probability Numerical Analysis 65C30, 60H35, 91G60, 17B22 |
| url | https://arxiv.org/abs/2410.10457 |