Ergodic control of diffusion processes
- Ari Arapostathis, Vivek S. Borkar, Mrinal K. Ghosh.
- Cambridge ; New York : Cambridge University Press, 2012.
- Physical description
- xvi, 323 p. ; 24 cm.
- Encyclopedia of mathematics and its applications ; v. 143.
Math & Statistics Library
QA274.75 .A73 2012
- Unknown QA274.75 .A73 2012
- Includes bibliographical references (p. -317) and indexes.
- 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.
- (source: Nielsen Book Data)
- Publisher's Summary
- 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.
(source: Nielsen Book Data)
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- Publication date
- Encyclopedia of mathematics and its applications ; 143
- 9780521768405 (hbk.)
- 0521768403 (hbk.)