Stochastic homogenization of deterministic control problems
نویسندگان
چکیده
In this paper we study homogenization of a class control problems in stationary and ergodic random environment. This problem has been mostly studied the calculus variations setting connection to Hamilton–Jacobi equation. We extend result with more general state dynamics macroscopically inhomogeneous Lagrangians. Moreover, our approach proves under weaker growth assumptions on Lagrangian, even well-studied setting.
منابع مشابه
Deterministic Approximation for Stochastic Control Problems
We consider a class of stochastic control problems where uncertainty is due to driving noises of general nature as well as to rapidly fluctuating processes affecting the drift. We show that, when the noise ”intensity” is small and the fluctuations become fast, the stochastic problems can be approximated by a deterministic one. We also show that the optimal control of the deterministic problem i...
متن کاملHomogenization of Some Low-Cost Control Problems
The aim of this article is to study the asymptotic behaviour of some low-cost control problems. These problems motivate the study of H-convergence with weakly converging data. An improved lower bound for the limit of energy functionals corresponding to weak data is established, in the periodic case. This fact is used to prove the Γconvergence of a low-cost problem with Dirichlet-type integral. ...
متن کاملHomogenization results for a deterministic multi-domains periodic control problem
We consider homogenization problems in the framework of deterministic optimal control when the dynamics and running costs are completely different in two (or more) complementary domains of the space R . For such optimal control problems, the three first authors have shown that several value functions can be defined, depending, in particular, of the choice is to use only “regular strategies” or ...
متن کاملOptimality of Deterministic Policies for Certain Stochastic Control Problems with Multiple Criteria and Constraints
For single-criterion stochastic control and sequential decision problems, optimal policies, if they exist, are typically nonrandomized. For problems with multiple criteria and constraints, optimal nonrandomized policies may not exist and, if optimal policies exist, they are typically randomized. In this paper we discuss certain conditions that lead to optimality of nonrandomized policies. In th...
متن کاملStochastic Homogenization of Reflected Stochastic Differential Equations
We investigate a functional limit theorem (homogenization) for Reflected Stochastic Differential Equations on a half-plane with stationary coefficients when it is necessary to analyze both the effective Brownian motion and the effective local time. We prove that the limiting process is a reflected non-standard Brownian motion. Beyond the result, this problem is known as a prototype of non-trans...
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: ESAIM: Control, Optimisation and Calculus of Variations
سال: 2021
ISSN: ['1262-3377', '1292-8119']
DOI: https://doi.org/10.1051/cocv/2021023