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.
- Markov property
- Markov selection theorem
- Measurable selection theorems
ASJC Scopus subject areas
- Applied Mathematics