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Existence of strong solutions for one-dimensional reflected mixed stochastic delay differential equations

  • Monir Chadad and Mohamed Erraoui EMAIL logo
Published/Copyright: March 26, 2024

Abstract

Relying on the pathwise uniqueness property, we prove existence of the strong solution of a one-dimensional reflected stochastic delay equation driven by a mixture of independent Brownian and fractional Brownian motions. The difficulty is that on the one hand we cannot use the fixed-point and contraction mapping methods because of the stochastic and pathwise integrals, and on the other hand the non-continuity of the Skorokhod map with respect to the norms considered.

MSC 2020: 34K50; 60G22; 60H05

Communicated by Maria Gordina


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Received: 2023-08-12
Revised: 2023-12-16
Published Online: 2024-03-26
Published in Print: 2025-02-01

© 2024 Walter de Gruyter GmbH, Berlin/Boston

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