• 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. 

References

SHOWING 1-10 OF 50 REFERENCES
The distance between the Kac process and the Wiener process with applications to generalized telegraph equations
In this note we obtain a local central limit theorem and an expansion of length two for the Kac processYα(t) that describes the position of a particle at timet after collisions. In particular, we
Optimal Transport
Point Process Calculus in Time and Space
Telegraph random evolutions on a circle.
On the exact distributions of the maximum of the asymmetric telegraph process
Estimation of Local Microcanonical Averages in Two Lattice Mean-Field Models Using Coupling Techniques
We consider an application of probabilistic coupling techniques which provides explicit estimates for comparison of local expectation values between label permutation invariant states, for instance,
An Invitation to Statistics in Wasserstein Space
Donsker-type theorem for BSDEs: Rate of convergence
In this paper, we study in the Markovian case the rate of convergence in the Wasserstein distance of an approximation of the solution to a BSDE given by a BSDE which is driven by a scaled random walk
Certain functionals of squared telegraph processes
We investigate the stochastic process defined as the square of the (integrated) symmetric telegraph process. Specifically, we obtain its probability law and a closed form expression of the moment
Telegraph Processes and Option Pricing
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.
...
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