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Ergodic Control of Diffusion Processes
Ari ArapostathisVivek S. BorkarMrinal K. Ghosh
出版Cambridge University Press, 2012
主題Mathematics / Probability & Statistics / GeneralMathematics / Probability & Statistics / Stochastic ProcessesMathematics / Transformations
ISBN05217684039780521768405
URLhttp://books.google.com.hk/books?id=HrtgjvzXBVwC&hl=&source=gbs_api
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註釋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.