Ergodic Control of Diffusion Processes

✍ Scribed by Ari Arapostathis, Vivek S. Borkar, Mrinal K. Ghosh

• Publisher: Cambridge University Press
• Year: 2012
• Tongue: English
• Leaves: 339
• Series: Encyclopedia of Mathematics and its Applications
• Edition: 0
• Category: Library

✦ Synopsis

This comprehensive volume on ergodic control for diffusions highlights intuition alongside technical arguments. A concise account of Markov process theory is followed by a complete development of the fundamental issues and formalisms in control of diffusions. This then leads to a comprehensive treatment of ergodic control, a problem that straddles stochastic control and the ergodic theory of Markov processes. The interplay between the probabilistic and ergodic-theoretic aspects of the problem, notably the asymptotics of empirical measures on one hand, and the analytic aspects leading to a characterization of optimality via the associated Hamilton-Jacobi-Bellman equation on the other, is clearly revealed. The more abstract controlled martingale problem is also presented, in addition to many other related issues and models. Assuming only graduate-level probability and analysis, the authors develop the theory in a manner that makes it accessible to users in applied mathematics, engineering, finance and operations research