A Note on Γ-Convergence of Monotone Functionals

  • Erick Treviño Aguilar
Conference paper
Part of the Progress in Probability book series (PRPR, volume 73)


In this note we present a criterion under which a functional defined on vectors of non-decreasing functions is the Γ-limit of a functional defined on vectors of continuous non-decreasing functions. To this end, we present a separation principle in which a weakly converging sequence of continuous non-decreasing functions is decomposed in two parts, one converging to a non-decreasing function with a finite number of jumps and the other to the complementary jumps.


Γ-Convergence Monotone functionals Singular control Skorokhod representation 

Mathematics Subject Classification

60B10 60B05 49J45 90C30 


  1. 1.
    P. Billingsley, Probability and Measure. Wiley Series in Probability and Mathematical Statistics, Anniversary edition (Wiley, New York, 2012)Google Scholar
  2. 2.
    A. Braides, A handbook of Γ-convergence, in Handbook of Differential Equations, Stationary Partial Differential Equations, ed. by M. Chipot, P. Quittner, vol. 2 (North-Holland, Amsterdam, 2006), pp. 101–213CrossRefGoogle Scholar
  3. 3.
    G. Buttazzo, G. Dal Maso, Gamma-convergence and optimal control problems. J. Optim. Theory Appl. 38(3), 385–407 (1982)MathSciNetCrossRefGoogle Scholar
  4. 4.
    G. Dal Maso, An Introduction to Gamma-Convergence (Birkhäuser, Boston, 1993)CrossRefGoogle Scholar
  5. 5.
    D. De Giorgi, Γ-convergenza e G-convergenza. Bollettino dell’ Unione Matematica Italiana 14, 213–220 (1977)MathSciNetzbMATHGoogle Scholar
  6. 6.
    S.N. Ethier, T.G. Kurtz, Markov Processes, Characterization and Convergence. Wiley Series in Probability and Mathematical Statistics (Wiley, New York, 1986)Google Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Erick Treviño Aguilar
    • 1
  1. 1.Department of Economics and FinanceUniversity of GuanajuatoGuanajuatoMexico

Personalised recommendations