Ergodicity of Robust Switching Control and Nonlinear System of Quasi-Variational Inequalities
Ergodicity of Robust Switching Control and Nonlinear System of Quasi-Variational Inequalities
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鲁棒切换控制的遍历性与拟变分不等式非线性系统
DOI：
10.1137/15m1023014
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发表时间：
2015
期刊：
影响因子：
--
通讯作者：
H. Pham
中科院分区：
文献类型：
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作者：
Erhan Bayraktar;Andrea Cosso;H. Pham
研究了一类完全非线性抛物型和椭圆型拟变分不等式组的渐近性态。这些方程与[3]中介绍的鲁棒切换控制问题有关。我们证明，随着时间的地平线走向无穷大（resp。贴现因子变为零）抛物系统的长期平均解（分别为椭圆系统的极限折扣解）的特征在于遍历变分不等式的非线性系统的解。我们的结果在耗散性条件下成立，并且对扩散项没有任何非退化假设。我们的方法主要使用概率参数，特别是一个双随机博弈表示的变分不等式系统的解决方案。
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 [3]. We prove that, as 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 non degeneracy 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.