Resumen del libro

Reseña: 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.

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indice: 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.

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