A stochastic Evans-Aronsson problem

By Diogo A. Gomes, Héctor Sánchez Morgado. 2013

60 citations recorded by the source corpus.

. In this paper the stochastic version of the Evans-Aronsson problem is studied. Both for the mechanical case and two dimensional problems we prove the existence of smooth solutions. We establish that the corresponding eﬀective Lagrangian and Hamiltonian are smooth. We study the limiting behavior and the convergence of the eﬀective Lagrangian and Hamiltonian, Mather measures and minimizers. We end the paper with applications to stationary mean-ﬁeld games.

Subfields: Finance, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/8cc1101d1c51b7255e0f9c91e4789e8e52b496a5

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Citations in the corpus

Time dependent mean-field games in the superquadratic case (2013, methodology): “Smooth solutions were studied in [22] (see also [26] for a related problem), [29, 31].”
Continuous Time Finite State Mean Field Games (2012, result): “We also discuss a variational formulation in analogy to the results in [GSM11] and [GPSM11], as well as some connections with partial differential equations, numerical methods and Hamilton-Jacobi equations.”
Regularity for second order stationary mean-field games (2015, background): “The existence of classical solutions for related systems is addressed in [16] and [20], whereas several a priori estimates are obtained in [15].”
Mean Field Games Models—A Brief Survey (2013, methodology): “In [42], the second-order case, which is associated with the noncoercive, convex functional was also studied and shown to admit smooth solutions which are minimizers of the above functional.”
On the existence of classical solutions for stationary extended mean field games (2013, methodology): “This application of the adjoint method extends the ideas in [GSM11].”