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2020 Generalized Peano problem with Lévy noise
Ilya Pavlyukevich, Andrey Pilipenko
Electron. Commun. Probab. 25: 1-14 (2020). DOI: 10.1214/20-ECP365

Abstract

We revisit the zero-noise Peano selection problem for Lévy-driven stochastic differential equation considered in [Pilipenko and Proske, Statist. Probab. Lett., 132:62–73, 2018] and show that the selection phenomenon pertains in the multiplicative noise setting and is robust with respect to certain perturbations of the irregular drift and of the small jumps of the noise.

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Ilya Pavlyukevich. Andrey Pilipenko. "Generalized Peano problem with Lévy noise." Electron. Commun. Probab. 25 1 - 14, 2020. https://doi.org/10.1214/20-ECP365

Information

Received: 28 November 2020; Accepted: 30 November 2020; Published: 2020
First available in Project Euclid: 30 December 2020

Digital Object Identifier: 10.1214/20-ECP365

Subjects:
Primary: 60H10
Secondary: 34A12 , 34E10 , 34F05 , 60F05 , 60G51

Keywords: irregular drift , Lévy process , non-uniqueness , Peano theorem , selection problem , Stochastic differential equation , zero noise limit

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