On ergodic stochastic control

DOI10.1080/03605309808821413zbMath1126.93434OpenAlexW1992759804MaRDI QIDQ4228070

Mariko Arisawa, Pierre-Louis Lions

Publication date: 1998

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03605309808821413

Mathematics Subject Classification ID

Dynamic programming in optimal control and differential games (49L20) Optimal stochastic control (93E20) Optimality conditions for problems involving randomness (49K45)

Related Items (65)

Long time averaged reflection force and homogenization of oscillating Neumann boundary conditions. ⋮ Long time asymptotics for fully nonlinear Bellman equations: a backward SDE approach ⋮ Quantitative stochastic homogenization of an unbounded front propagation problem ⋮ Ergodic BSDEs and related PDEs with Neumann boundary conditions ⋮ Liouville properties and critical value of fully nonlinear elliptic operators ⋮ Some homogenization results for non-coercive Hamilton-Jacobi equations ⋮ Viscosity methods for large deviations estimates of multiscale stochastic processes ⋮ Tauberian theorem for value functions ⋮ Discontinuous Galerkin and C⁰-IP finite element approximation of periodic Hamilton–Jacobi–Bellman–Isaacs problems with application to numerical homogenization ⋮ Ergodic BSDEs driven by G-Brownian motion and applications ⋮ LP-related representations of Cesàro and Abel limits of optimal value functions ⋮ The ergodic limit for weak solutions of elliptic equations with Neumann boundary condition ⋮ A uniform Tauberian theorem in dynamic games ⋮ Long term average cost control problems without ergodicity ⋮ Linear programming estimates for Cesàro and Abel limits of optimal values in optimal control problems ⋮ Linear programming formulation of long-run average optimal control problem ⋮ Ergodic control of multi-class \(\mathrm{M}/\mathrm{M}/N+\mathrm{M}\) queues in the Halfin-Whitt regime ⋮ Ergodic maximum principle for stochastic systems ⋮ Rate of convergence for singular perturbations of Hamilton-Jacobi equations in unbounded spaces ⋮ On the vanishing discount approximation for compactly supported perturbations of periodic Hamiltonians: the 1d case ⋮ Gradient bounds for nonlinear degenerate parabolic equations and application to large time behavior of systems ⋮ Coupling by reflection for controlled diffusion processes: turnpike property and large time behavior of Hamilton-Jacobi-Bellman equations ⋮ A continuous dependence estimate for viscous Hamilton-Jacobi equations on networks with applications ⋮ A Viscous Ergodic Problem with Unbounded and Measurable Ingredients, Part 1: HJB Equation ⋮ Ergodic control of McKean-Vlasov SDEs and associated Bellman equation ⋮ Large deviations for multiscale diffusion via weak convergence methods ⋮ Large deviations and importance sampling for systems of slow-fast motion ⋮ An eikonal equation with vanishing Lagrangian arising in global optimization ⋮ Continuous dependence estimates and homogenization of quasi-monotone systems of fully nonlinear second order parabolic equations ⋮ Representation of asymptotic values for nonexpansive stochastic control systems ⋮ Representation Formulas for Limit Values of Long Run Stochastic Optimal Controls ⋮ Large-time asymptotics for one-dimensional Dirichlet problems for Hamilton-Jacobi equations with noncoercive Hamiltonians ⋮ Representation of limit values for nonexpansive stochastic differential games ⋮ Continuous dependence estimates for the ergodic problem of Bellman equation with an application to the rate of convergence for the homogenization problem ⋮ Nonexistence of nonconstant solutions of some degenerate Bellman equations and applications to stochastic control ⋮ On representation formulas for long run averaging optimal control problem ⋮ On cell problems for Hamilton-Jacobi equations with non-coercive Hamiltonians and their application to homogenization problems ⋮ Multiscale problems and homogenization for second-order Hamilton-Jacobi equations ⋮ Nonlinear elliptic systems and mean-field games ⋮ The ergodic problem for some subelliptic operators with unbounded coefficients ⋮ Stochastic homogenization of a front propagation problem with unbounded velocity ⋮ Ergodic behavior of control and mean field games problems depending on acceleration ⋮ A representation theorem for the viscosity solutions of a degenerate ergodic Hamilton-Jacobi-Bellman equation on the torus ⋮ Stochastic homogenization of interfaces moving with changing sign velocity ⋮ The ``ergodic limit for a viscous Hamilton-Jacobi equation with Dirichlet conditions ⋮ Some recent aspects of differential game theory ⋮ Ergodic BSDEs under weak dissipative assumptions ⋮ Ergodicity of Hamilton-Jacobi equations with a noncoercive nonconvex Hamiltonian in \(\mathbb R^2/\mathbb Z^2\) ⋮ Lipschitz regularity results for nonlinear strictly elliptic equations and applications ⋮ Homogenization for fully nonlinear parabolic equations ⋮ Homogenization and enhancement for the \(G\)-equation ⋮ On ergodic problem for Hamilton-Jacobi-Isaacs equations ⋮ Asymptotics of values in dynamic games on large intervals ⋮ On almost periodic viscosity solutions to Hamilton-Jacobi equations ⋮ Existence of asymptotic values for nonexpansive stochastic control systems ⋮ On Differential Games with Long-Time-Average Cost ⋮ LP Formulations of Discrete Time Long-Run Average Optimal Control Problems: The NonErgodic Case ⋮ Singular perturbations and optimal control of stochastic systems in infinite dimension: HJB equations and viscosity solutions ⋮ Vanishing Discount Limit and Nonexpansive Optimal Control and Differential Games ⋮ Asymptotic Control for a Class of Piecewise Deterministic Markov Processes Associated to Temperate Viruses ⋮ On the decay of viscosity solutions to Hamilton–Jacobi equations with almost periodic initial data ⋮ On the boundary ergodic problem for fully nonlinear equations in bounded domains with general nonlinear Neumann boundary conditions ⋮ Homogenization of degenerate second-order PDE in periodic and almost periodic environments and applications ⋮ Multi-population mean field games systems with Neumann boundary conditions ⋮ Ergodicity of Robust Switching Control and Nonlinear System of Quasi-Variational Inequalities

Cites Work

• Unnamed Item
• Viscosity solutions of fully nonlinear second-order elliptic partial differential equations
• Linear oblique derivative problems for the uniformly elliptic Hamilton- Jacobi-Bellman equation
• Neumann type boundary conditions for Hamilton-Jacobi equations
• Long time averaged reflection force and homogenization of oscillating Neumann boundary conditions.
• Optimal control of diffustion processes and hamilton-jacobi-bellman equations part I: the dynamic programming principle and application
• On Some Impulse Control Problems with Long Run Average Cost
• User’s guide to viscosity solutions of second order partial differential equations

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