The vanishing discount problem and viscosity Mather measures. Part 1: the problem on a torus

By Hitoshi Ishii, Hiroyoshi Mitake, Hung Vinh Tran. 2016

58 citations recorded by the source corpus.

We develop a variational approach to the vanishing discount problem for fully nonlinear, degenerate elliptic, partial differential equations. Under mild assumptions, we introduce viscosity Mather measures for such partial differential equations, which are natural extensions of the Mather measures. Using the viscosity Mather measures, we prove that the whole family of solutions $v^\lambda$ of the discount problem with the factor $\lambda>0$ converges to a solution of the ergodic problem as $\lambda \to 0$.

Subfields: Applied Mathematics, Finance, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/8180ab2627253fb35a062bc2cb0adc80e1c2dc8b

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Dipmat
2. Alessio Porretta Ceremade
3. Pierre Cardaliaguet
4. P. J. Graber
5. Daniel Lacker
6. Diogo A. Gomes
7. Edgard A. Pimentel
8. João Saúde

In Finance

1. Dipmat
2. Alessio Porretta Ceremade
3. Pierre Cardaliaguet
4. Daniel Lacker
5. P. J. Graber
6. Diogo A. Gomes
7. Charles Bertucci
8. Alessio Porretta

In Mathematical Physics

1. Dipmat
2. Alessio Porretta Ceremade
3. Pierre Cardaliaguet

Citations in the corpus

• Long time behavior of the master equation in mean field game theory (2017, methodology): “The result has been generalized to the second order HJ setting by Mitake and Tran [22] (see also Mitake and Tran [23] and Ishii, Mitake and Tran [16]).”