Ergodic Control of Diffusion Processes

Erscheinungsjahr 2011
ISBN: 978-0-521-76840-5
Verlag: Cambridge University Press

Buch, Englisch, Band 143, 340 Seiten, Format (B × H): 161 mm x 240 mm, Gewicht: 675 g

Reihe: Encyclopedia of Mathematics and its Applications

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.

Autoren/Hrsg.

Arapostathis, Ari

Borkar, Vivek S.

Ghosh, Mrinal K.

Fachgebiete

• Mathematik | Informatik Mathematik Operations Research
• Mathematik | Informatik Mathematik Stochastik Stochastische Prozesse
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle

Inhaltsverzeichnis

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.

Über Autor(innen)

Borkar, Vivek S.
Vivek S. Borkar is a Senior Professor in the School of Technology and Computer Science at the Tata Institute of Fundamental Research in Mumbai.

Arapostathis, Ari
Ari Arapostathis is a Professor in the Department of Electrical and Computer Engineering at the University of Texas, Austin.

Ghosh, Mrinal K.
Mrinal K. Ghosh is a Professor in the Department of Mathematics at the Indian Institute of Science in Bangalore.

Ari Arapostathis is a Professor in the Department of Electrical and Computer Engineering at the University of Texas, Austin.

Vivek S. Borkar is a Senior Professor in the School of Technology and Computer Science at the Tata Institute of Fundamental Research in Mumbai.

Mrinal K. Ghosh is a Professor in the Department of Mathematics at the Indian Institute of Science in Bangalore.