Semiflow selection and markov selection theorems

Jorge E. Cardona, Lev Kapitanski

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

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 natu-rally 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.

Original languageEnglish (US)
Pages (from-to)197-227
Number of pages31
JournalTopological Methods in Nonlinear Analysis
Volume56
Issue number1
DOIs
StatePublished - 2020

Keywords

  • Markov property
  • Markov selection theorem
  • Measurable selection theorems
  • Semiflows

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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