In this paper we discuss the properties of particular set-valued maps in the space of probability measures on a finite-dimensional space that are con- structed by mean of a suitable lift of set-valued map in the underlying space. In particular, we are interested to establish under which conditions some good regularity properties of the original set-valued map are inherited by the lifted one. The main motivation for the study is represented by multi-agent systems, i.e., finite-dimensional systems where the number of (microscopic) agents is so large that only macroscopical description are actually available. The macroscop- ical behaviour is thus expressed by the superposition of the behaviours of the microscopic agents. Using the common description of the state of a multi-agent system by mean of a time-dependent probability measure, expressing the fraction of agents contained in a region at a given time moment, the results of this paper yield regularity results for the macroscopical behaviour of the system.

Random Lifting of Set-Valued Maps

Marigonda, Antonio;
2022

Abstract

In this paper we discuss the properties of particular set-valued maps in the space of probability measures on a finite-dimensional space that are con- structed by mean of a suitable lift of set-valued map in the underlying space. In particular, we are interested to establish under which conditions some good regularity properties of the original set-valued map are inherited by the lifted one. The main motivation for the study is represented by multi-agent systems, i.e., finite-dimensional systems where the number of (microscopic) agents is so large that only macroscopical description are actually available. The macroscop- ical behaviour is thus expressed by the superposition of the behaviours of the microscopic agents. Using the common description of the state of a multi-agent system by mean of a time-dependent probability measure, expressing the fraction of agents contained in a region at a given time moment, the results of this paper yield regularity results for the macroscopical behaviour of the system.
978-3-030-97548-7
Set-valued map
Multi-agent systems
Statistical description
File in questo prodotto:
File Dimensione Formato  
Random lifting of set-valued maps_Capuani_Marigonda_Mogentale.pdf

embargo fino al 31/03/2023

Descrizione: post-print
Tipologia: Documento in Post-print
Licenza: Accesso ristretto
Dimensione 329.64 kB
Formato Adobe PDF
329.64 kB Adobe PDF   Visualizza/Apri   Richiedi una copia
Capuani2022_Chapter_RandomLiftingOfSet-ValuedMaps.pdf

embargo fino al 31/03/2023

Descrizione: fulltext
Tipologia: Documento in Post-print
Licenza: Accesso ristretto
Dimensione 248.44 kB
Formato Adobe PDF
248.44 kB Adobe PDF   Visualizza/Apri   Richiedi una copia

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11562/1059873
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 0
  • ???jsp.display-item.citation.isi??? ND
social impact