Wasserstein error estimates between telegraph processes and Brownian motion

Fuente: arXiv
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Hauptverfasser: Barrera, Gerardo, Lukkarinen, Jani, Pakkanen, Mikko S.
Format: Preprint
Veröffentlicht: 2025
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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