2001/04/24 by Diogo A. Gomes, Diogo Aguiar Gomes, Gomes, Diogo Aguiar · 2 citations
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #35J60 #49L25 #Analysis of PDEs (math.AP) #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Optimization and Control (math.OC) #Quantum chaos and dynamical systems #Stochastic processes and financial applications #math.AP #math.DS #math.OC #msc:35J60 #msc:49L25
paper · pdf · doi:10.48550/arxiv.math/0104230
arxiv created 2001/04/24 · openalex publication_date 2001/04/24 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we discuss a stochastic analog of Aubry-Mather theory in which a deterministic control problem is replaced by a controlled diffusion. We prove the existence of a minimizing measure (Mather measure) and discuss its main properties using viscosity solutions of Hamilton-Jacobi equations. Then we prove regularity estimates on viscosity solutions of Hamilton-Jacobi equation using the Mather measure. Finally we apply these results to prove asymptotic estimates on the trajectories of controlled diffusions and study the convergence of Mather measures as the rate of diffusion vanishes.