Ergodic control of diffusion processes
β Ari Arapostathis; Vivek S Borkar; Mrinal K Ghosh
π Library
π
2011
π Cambridge University Press
π English
β¦ LIBER β¦
π
Ergodic Control of Diffusion Processes
β Scribed by Ari Arapostathis, Vivek S. Borkar, Mrinal K. Ghosh
- Publisher
- Cambridge University Press
- Year
- 2012
- Tongue
- English
- Leaves
- 339
- Series
- Encyclopedia of Mathematics and its Applications
- Edition
- 1
- Category
- Library
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β¦ Synopsis
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.
β¦ Table of Contents
Frontmatter......Page 1
Contents......Page 7
Preface......Page 11
Frequently Used Notation......Page 15
1 - Markov Processes and Ergodic Properties......Page 17
2 - Controlled Diffusions......Page 46
3 - Nondegenerate Controlled Diffusions......Page 102
4 - Various Topics in Nondegenerate Diffusions......Page 170
5 - Controlled Switching Diffusions......Page 210
6 - Controlled Martingale Problems......Page 233
7 - Degenerate Controlled Diffusions......Page 269
8 - Controlled Diffusions with Partial Observations......Page 295
Epilogue......Page 316
Appendix: Results from Second Order Elliptic Equations......Page 319
References......Page 327
Index of symbols......Page 335
Subject index......Page 337
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