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2020 Semiflow selection and Markov selection theorems
Jorge E. Cardona, Lev Kapitanski
Topol. Methods Nonlinear Anal. 56(1): 197-227 (2020). DOI: 10.12775/TMNA.2020.010

Abstract

The deterministic analog of the Markov property of a time-homogeneous Markov process is the semigroup property of solutions of an autonomous differential equation. The semigroup property arises naturally when the solutions of a differential equation are unique, and leads to a semiflow. We prove an abstract result on the measurable selection of a semiflow for the situations without uniqueness. We outline applications to ODEs, PDEs, differential inclusions, etc. Our proof of the semiflow selection theorem is motivated by N.V. Krylov's Markov selection theorem. To accentuate this connection, we include a new version of the Markov selection theorem related to more recent papers of Flandoli, Romito and Goldys et al.

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Jorge E. Cardona. Lev Kapitanski. "Semiflow selection and Markov selection theorems." Topol. Methods Nonlinear Anal. 56 (1) 197 - 227, 2020. https://doi.org/10.12775/TMNA.2020.010

Information

Published: 2020
First available in Project Euclid: 16 October 2020

MathSciNet: MR4175077
Digital Object Identifier: 10.12775/TMNA.2020.010

Rights: Copyright © 2020 Juliusz P. Schauder Centre for Nonlinear Studies

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Vol.56 • No. 1 • 2020
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