Book2011

Ergodic Control of Diffusion Processes

Ari Arapostathis · Vivek S. Borkar · Mrinal K. Ghosh

177 citations0/0 files storedCambridge University Press eBooks

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Stochastic processes and financial applications Stochastic processes and statistical mechanics Adaptive Dynamic Programming Control

Abstract

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.

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References

2007Brownian Motion and Stochastic Calculus 1983Stochastic Differential Equations and Diffusion Processes 1990Numerical Methods for Stochastic Control Problems in Continuous Time 1976Stochastic Differential Equations and Applications 1980Controlled Diffusion Processes 1984Stochastic differential equations with reflecting boundary conditions 1974A TRANSFORMATION OF THE PHASE SPACE OF A DIFFUSION PROCESS THAT REMOVES THE DRIFT 1996Existence of strong solutions for Itô's stochastic equations via approximations

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