ERGODICITY OF ROBUST SWITCHING CONTROL AND NONLINEAR SYSTEM OF QUASI-VARIATIONAL INEQUALITIES

作者：Bayraktar Erhan; Coss Andrea; Pham Huyen

来源：SIAM Journal on Control and Optimization, 2017, 55(3): 1915-1953.

DOI：10.1137/15M1023014

• optimal switching
• system of quasi-variational inequalities
• stochastic games
• ergodic problem
• randomization

We analyze the asymptotic behavior for a system of fully nonlinear parabolic and elliptic quasi-variational inequalities. These equations are related to robust switching control problems introduced in [E. Bayraktar, A. Cosso, and H. Pham, SIAM J. Control Optim., 54 (2016), pp. 2594-2628]. We prove that, as the time horizon goes to infinity (resp., discount factor goes to zero), the long run average solution to the parabolic system (resp., the limiting discounted solution to the elliptic system) is characterized by a solution of a nonlinear system of ergodic variational inequalities. Our results hold under a dissipativity condition and without any nondegeneracy assumption on the diffusion term. Our approach uses mainly probabilistic arguments and in particular a dual randomized game representation for the solution to the system of variational inequalities.

• 出版日期2017