Occupation measures for controlled Markov processes: Characterization and optimality

• 成果类型: Article
• 署名作者: Bhati, AG; Borkar, VS
• 署名单位: Indian Institute of Science (IISC) - Bangalore
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• 发表日期: 1996
• 页码: 1531-1562
• 关键词: stochastic-control problems; time-average control; martingale problems; extremal solutions; evolution-equations; DIFFUSIONS; EXISTENCE

摘要

For controlled Markov processes taking values in a Polish space, control problems with ergodic cost, infinite-horizon discounted cost and finite-horizon cost are studied. Each is posed as a convex optimization problem wherein one tries to minimize a linear functional on a closed convex set of appropriately defined occupation measures for the problem. These are characterized as solutions of a linear equation asssociated with the problem. This characterization is used to establish the existence of optimal Markov controls. The dual convex optimization problem is also studied.