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Corpus ID: 245650804

Quantitative control of Wasserstein distance between Brownian motion and the Goldstein--Kac telegraph process

@inproceedings{Barrera2022QuantitativeCO,
title={Quantitative control of Wasserstein distance between Brownian motion and the Goldstein--Kac telegraph process},
author={Gerardo Barrera and Jani Lukkarinen},
year={2022}
}

In this manuscript, we provide a non-asymptotic process level control between the telegraph process and the Brownian motion with suitable diffusivity constant via a Wasserstein distance with quadratic average cost. In addition, we derive non-asymptotic estimates for the corresponding time average p-th moments. The proof relies on coupling techniques such as coinflip coupling, synchronous coupling and the Komlós–Major–Tusnády coupling.

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Preface.- 1.Preliminaries.- 2.Telegraph Process on the Line.- 3.Functionals of Telegraph Process.- 4.Asymmetric Jump-Telegraph Processes.- 5.Financial Modelling and Option Pricing.- Index.