02437nam a22003738a 4500 CR9781139003605 UkCbUP 20180107143414.0 m|||||o||d|||||||| cr|||||||||||| 110124s2011||||enk s ||1 0|eng|d 9781139003605 (ebook) 9780521768405 (hardback) UkCbUP UkCbUP rda QA274.75 .A73 2012 519.2/33 23 Arapostathis, Ari, author. Ergodic Control of Diffusion Processes / [electronic resource] Ari Arapostathis, Vivek S. Borkar, Mrinal K. Ghosh. Cambridge : Cambridge University Press, 2011. 1 online resource (340 pages) : digital, PDF file(s). text txt rdacontent computer c rdamedia online resource cr rdacarrier Encyclopedia of Mathematics and its Applications ; no. 143 Title from publisher's bibliographic system (viewed on 09 Oct 2015). 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. Diffusion processes Ergodic theory Borkar, Vivek S., author. Ghosh, Mrinal K., author. Print version: 9780521768405 Encyclopedia of Mathematics and its Applications ; no. 143. http://dx.doi.org/10.1017/CBO9781139003605 Cambridge Books Online 236640 236640