Wasserstein error estimates between telegraph processes and Brownian motion
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Abstract
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.Keywords
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This publication has 51 references indexed in Scilit:
- On the Telegraph Process Driven by Geometric Counting Process with Poisson-Based ResettingJournal of Statistical Physics, 2023
- On Some Finite-Velocity Random Motions Driven by the Geometric Counting ProcessJournal of Statistical Physics, 2023
- Lectures on Optimal Transport2021
- Probability Theory2020
- An Invitation to Statistics in Wasserstein Space2020
- Telegraph Process on the Line2013
- Optimal Transport2009
- Aspects of Brownian Motion2008
- Brownian Motion, Obstacles and Random Media1998
- The distance between the Kac process and the Wiener process with applications to generalized telegraph equationsJournal of Theoretical Probability, 1990