Wasserstein error estimates between telegraph processes and Brownian motion
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866916950039330816 |
|---|---|
| author | Barrera, Gerardo Lukkarinen, Jani Pakkanen, Mikko S. |
| author_facet | Barrera, Gerardo Lukkarinen, Jani Pakkanen, Mikko S. |
| contents | We provide non-asymptotic error bounds in the path Wasserstein distance with quadratic integral cost between suitable functionals of the telegraph process and the corresponding functional of Brownian motion with explicit diffusivity constant. These results cover, in particular, the well-known example of the exponential integral functional of the geometric Brownian motion. The non-asymptotic error bounds tend to zero in the so-called Kac regime. Moreover, the error bounds remain valid when the flip rate for the telegraph process is small. We assess the sharpness of the error bounds through numerical experiments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_11871 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Wasserstein error estimates between telegraph processes and Brownian motion Barrera, Gerardo Lukkarinen, Jani Pakkanen, Mikko S. Probability Mathematical Physics 60G50, 60J65, Secondary 60G50, 60J65, 35L99, 60K50 We provide non-asymptotic error bounds in the path Wasserstein distance with quadratic integral cost between suitable functionals of the telegraph process and the corresponding functional of Brownian motion with explicit diffusivity constant. These results cover, in particular, the well-known example of the exponential integral functional of the geometric Brownian motion. The non-asymptotic error bounds tend to zero in the so-called Kac regime. Moreover, the error bounds remain valid when the flip rate for the telegraph process is small. We assess the sharpness of the error bounds through numerical experiments. |
| title | Wasserstein error estimates between telegraph processes and Brownian motion |
| topic | Probability Mathematical Physics 60G50, 60J65, Secondary 60G50, 60J65, 35L99, 60K50 |
| url | https://arxiv.org/abs/2509.11871 |