A Note on Γ-Convergence of Monotone Functionals
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.
KeywordsΓ-Convergence Monotone functionals Singular control Skorokhod representation
Mathematics Subject Classification60B10 60B05 49J45 90C30
- 1.P. Billingsley, Probability and Measure. Wiley Series in Probability and Mathematical Statistics, Anniversary edition (Wiley, New York, 2012)Google Scholar
- 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