Electronic Communications in Probability

Generalized Peano problem with Lévy noise

Ilya Pavlyukevich and Andrey Pilipenko

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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.

Article information

Electron. Commun. Probab., Volume 25 (2020), paper no. 85, 14 pp.

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

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Primary: 60H10: Stochastic ordinary differential equations [See also 34F05]
Secondary: 60F05: Central limit and other weak theorems 60G51: Processes with independent increments; Lévy processes 34A12: Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions 34E10: Perturbations, asymptotics 34F05: Equations and systems with randomness [See also 34K50, 60H10, 93E03]

Lévy process stochastic differential equation selection problem zero noise limit Peano theorem non-uniqueness irregular drift

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Pavlyukevich, Ilya; Pilipenko, Andrey. Generalized Peano problem with Lévy noise. Electron. Commun. Probab. 25 (2020), paper no. 85, 14 pp. doi:10.1214/20-ECP365. https://projecteuclid.org/euclid.ecp/1609319090

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