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.
• A modern, coherent treatment of scattered results on ergodic control • Contains new and improved results at the cutting edge of research • Written by three primary contributors in the field
Contents
Preface; Frequently used notation; 1. Markov processes and ergodic properties; 2. Controlled diffusions; 3. Nondegenerate controlled diffusions; 4. Various topics in nondegenerate diffusions; 5. Controlled switching diffusions; 6. Controlled martingale problems; 7. Degenerate controlled diffusions; 8. Controlled diffusions with partial observations; Epilogue; Appendix; References; Index of symbols; Subject index.
Review
'Assuming good knowledge in analysis, probability theory and stochastic processes, [this book provides] a careful and comprehensive treatment of ergodic control of diffusion processes.' Kurt Marti, Zentralblatt MATH
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