Limits of random walks with distributionally robust transition probabilities

Bartl, Daniel; Eckstein, Stephan; Kupper, Michael

Limits of random walks with distributionally robust transition probabilities

Dateien

Bartl_2-xruc5joqc0wy2.pdfGröße: 301.37 KBDownloads: 144

Datum

2021

Open Access-Veröffentlichung

Open Access Gold

Sammlungen

Mathematik und Statistik

Publikationstyp

Zeitschriftenartikel

Publikationsstatus

Published

Erschienen in

Electronic Communications in Probability. Institute of Mathematical Statistics (IMS). 2021, 26, 28. eISSN 1083-589X. Available under: doi: 10.1214/21-ECP393

Zusammenfassung

We consider a nonlinear random walk which, in each time step, is free to choose its own transition probability within a neighborhood (w.r.t. Wasserstein distance) of the transition probability of a fixed Lévy process. In analogy to the classical framework we show that, when passing from discrete to continuous time via a scaling limit, this nonlinear random walk gives rise to a nonlinear semigroup. We explicitly compute the generator of this semigroup and corresponding PDE as a perturbation of the generator of the initial Lévy process.

Fachgebiet (DDC)

510 Mathematik

Schlagwörter

nonlinear Lévy processes; Wasserstein distance; scaling limit

Zitieren

ISO 690

BARTL, Daniel, Stephan ECKSTEIN, Michael KUPPER, 2021. Limits of random walks with distributionally robust transition probabilities. In: Electronic Communications in Probability. Institute of Mathematical Statistics (IMS). 2021, 26, 28. eISSN 1083-589X. Available under: doi: 10.1214/21-ECP393

BibTex

@article{Bartl2021Limit-53981,
  year={2021},
  doi={10.1214/21-ECP393},
  title={Limits of random walks with distributionally robust transition probabilities},
  volume={26},
  journal={Electronic Communications in Probability},
  author={Bartl, Daniel and Eckstein, Stephan and Kupper, Michael},
  note={Article Number: 28}
}

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Universitätsbibliographie

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