Publikation: Limits of random walks with distributionally robust transition probabilities
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2021
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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.
Zusammenfassung in einer weiteren Sprache
Fachgebiet (DDC)
510 Mathematik
Schlagwörter
nonlinear Lévy processes; Wasserstein distance; scaling limit
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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-ECP393BibTex
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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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<dcterms:abstract xml:lang="eng">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.</dcterms:abstract>
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