Stochastic Perron's Method for Hamilton--Jacobi--Bellman Equations
نویسندگان
چکیده
منابع مشابه
Stochastic Perron's method for Hamilton-Jacobi-Bellman equations
We show that the value function of a stochastic control problem is the unique solution of the associated Hamilton-Jacobi-Bellman (HJB) equation, completely avoiding the proof of the so-called dynamic programming principle (DPP). Using Stochastic Perron's method we construct a super-solution lying below the value function and a sub-solution dominating it. A comparison argument easily closes the ...
متن کاملHamilton-Jacobi-Bellman Equations
This work treats Hamilton-Jacobi-Bellman equations. Their relation to several problems in mathematics is presented and an introduction to viscosity solutions is given. The work of several research articles is reviewed, including the Barles-Souganidis convergence argument and the inaugural papers on mean-field games. Original research on numerical methods for Hamilton-Jacobi-Bellman equations is...
متن کاملVerification Theorems for Hamilton--Jacobi--Bellman Equations
We study an optimal control problem in Bolza form and we consider the value function associated to this problem. We prove two verification theorems which ensure that, if a function W satisfies some suitable weak continuity assumptions and a Hamilton-Jacobi-Bellman inequality outside a countably H-rectifiable set, then it is lower or equal to the value function. These results can be used for opt...
متن کاملMultigrid Methods for Hamilton-Jacobi-Bellman and Hamilton-Jacobi-Bellman-Isaacs Equations
We propose multigrid methods for solving Hamilton-Jacobi-Bellman (HJB) and HamiltonJacobi-Bellman-Isaacs (HJBI) equations. The methods are based on the full approximation scheme. We propose a damped-relaxation method as smoother for multigrid. In contrast with policy iteration, the relaxation scheme is convergent for both HJB and HJBI equations. We show by local Fourier analysis that the damped...
متن کاملMultigrid Methods for Second Order Hamilton-Jacobi-Bellman and Hamilton-Jacobi-Bellman-Isaacs Equations
We propose multigrid methods for solving the discrete algebraic equations arising from the discretization of the second order Hamilton–Jacobi–Bellman (HJB) and Hamilton– Jacobi–Bellman–Isaacs (HJBI) equations. We propose a damped-relaxation method as a smoother for multigrid. In contrast with the standard policy iteration, the proposed damped-relaxation scheme is convergent for both HJB and HJB...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: SIAM Journal on Control and Optimization
سال: 2013
ISSN: 0363-0129,1095-7138
DOI: 10.1137/12090352x