On a Boltzmann mean field model for knowledge growth

Beitrag in einer Fachzeitschrift


Details zur Publikation

Autorinnen und Autoren: Burger M, Lorz A, Wolfram MT
Zeitschrift: SIAM Journal on Applied Mathematics
Verlag: Society for Industrial and Applied Mathematics Publications
Jahr der Veröffentlichung: 2016
Band: 76
Seitenbereich: 1799-1818
ISSN: 0036-1399


Abstract

In this paper we analyze a Boltzmann-type mean field game model for knowledge growth, which was proposed by Lucas et al. [J. Political Econ., 122 (2014), pp. 1-51]. We discuss the underlying mathematical model, which consists of a coupled system of a Boltzmann-type equation for the agent density and a Hamilton-Jacobi-Bellman equation for the optimal strategy. We study the analytic features of each equation separately and show local in time existence and uniqueness for the fully coupled system. Furthermore we focus on the construction and existence of special solutions, which relate to exponential growth in time - so-called balanced growth path solutions. Finally, we illustrate the behavior of solutions for the full system and the balanced growth path equations with numerical simulations.


Einrichtungen weiterer Autorinnen und Autoren

University of Paris 6 - Pierre et Marie Curie / Université Paris VI Pierre et Marie Curie (UPMC)
University of Warwick
Westfälische Wilhelms-Universität (WWU) Münster


Zitierweisen

APA:
Burger, M., Lorz, A., & Wolfram, M.-T. (2016). On a Boltzmann mean field model for knowledge growth. SIAM Journal on Applied Mathematics, 76, 1799-1818. https://dx.doi.org/10.1137/15M1018599

MLA:
Burger, Martin, Alexander Lorz, and Marie-Therese Wolfram. "On a Boltzmann mean field model for knowledge growth." SIAM Journal on Applied Mathematics 76 (2016): 1799-1818.

BibTeX: 

Zuletzt aktualisiert 2018-03-12 um 12:38