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Monotone solutions for mean field games master equations : finite state space and optimal stopping
- Source :
- Journal de l'École polytechnique — Mathématiques, Journal de l'École polytechnique — Mathématiques, École polytechnique, 2021, 8, pp.1099-1132
- Publication Year :
- 2020
- Publisher :
- arXiv, 2020.
-
Abstract
- International audience; We present a new notion of solution for mean field games master equations. This notion allows us to work with solutions which are merely continuous. We prove first results of uniqueness and stability for such solutions. It turns out that this notion is helpful to characterize the value function of mean field games of optimal stopping or impulse control and this is the topic of the second half of this paper. The notion of solution we introduce is only useful in the monotone case. We focus in this paper in the finite state space case.
- Subjects :
- General Mathematics
010102 general mathematics
Stability (learning theory)
Space (mathematics)
01 natural sciences
010101 applied mathematics
Mathematics - Analysis of PDEs
Monotone polygon
Mean field theory
Bellman equation
Master equation
FOS: Mathematics
[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]
Applied mathematics
Optimal stopping
Uniqueness
0101 mathematics
Mathematics
Analysis of PDEs (math.AP)
Subjects
Details
- ISSN :
- 24297100 and 2270518X
- Database :
- OpenAIRE
- Journal :
- Journal de l'École polytechnique — Mathématiques, Journal de l'École polytechnique — Mathématiques, École polytechnique, 2021, 8, pp.1099-1132
- Accession number :
- edsair.doi.dedup.....96ec38244052a6d7d3836ed627fb22c0
- Full Text :
- https://doi.org/10.48550/arxiv.2007.11854