Ergodic Control Of Diffusion Processes
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Ergodic Control of Diffusion Processes
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.
Ergodic Control of Diffusion Processes
Author: Ari Arapostathis
language: en
Publisher: Cambridge University Press
Release Date: 2012
The first comprehensive account of controlled diffusions with a focus on ergodic or 'long run average' control.
Diffusion Processes and their Sample Paths
Author: Kiyosi Itô
language: en
Publisher: Springer Science & Business Media
Release Date: 1996-01-05
Since its first publication in 1965 in the series Grundlehren der mathematischen Wissenschaften this book has had a profound and enduring influence on research into the stochastic processes associated with diffusion phenomena. Generations of mathematicians have appreciated the clarity of the descriptions given of one- or more- dimensional diffusion processes and the mathematical insight provided into Brownian motion. Now, with its republication in the Classics in Mathematics it is hoped that a new generation will be able to enjoy the classic text of Itô and McKean.