Ergodic Control of Diffusion Processes EPUB

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.