Ergodic Control of Diffusion Processes

Ergodic Control of Diffusion Processes

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Description

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.show more

Product details

  • Electronic book text
  • CAMBRIDGE UNIVERSITY PRESS
  • Cambridge University Press (Virtual Publishing)
  • Cambridge, United Kingdom
  • English
  • 1 b/w illus.
  • 1139003607
  • 9781139003605

Review quote

'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 MATHshow more

Table of 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.show more