## Controlled Markov Processes and Viscosity SolutionsThis book is intended as an introduction to optimal stochastic control for continuous time Markov processes and to the theory of viscosity solutions. |

### From inside the book

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Page 1

If the goal is to optimize some payoff function ( or cost function , which depends on the

If the goal is to optimize some payoff function ( or cost function , which depends on the

**control**inputs to the system , then the**problem**is one of optimal**control**. In this introductory chapter we are concerned with deterministic ...Page 315

VIII Singular Stochastic Control VIII.1 Introduction In contrast to classical

VIII Singular Stochastic Control VIII.1 Introduction In contrast to classical

**control problems**, in which the ... BatherChernoff were the first to formulate such a problem in their study of a simplified model of spacecraft control .Page 362

VIII.9 Historical remarks The first examples of stochastic singular

VIII.9 Historical remarks The first examples of stochastic singular

**control problems**were formulated by Bather and Chernoff ( BC1-2 ) . ... One dimensional convex problem received much attention in the early 1980's .### What people are saying - Write a review

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### Contents

Viscosity Solutions | 53 |

Controlled Markov Diffusions in R | 157 |

SecondOrder Case | 213 |

Copyright | |

7 other sections not shown

### Other editions - View all

Controlled Markov Processes and Viscosity Solutions Wendell H. Fleming,Halil Mete Soner Limited preview - 2006 |

Controlled Markov Processes and Viscosity Solutions Wendell H. Fleming,Halil Mete Soner No preview available - 2006 |

### Common terms and phrases

admissible apply approximation assume assumptions boundary condition bounded calculus called Chapter compact condition consider constant continuous control problem convergence convex Corollary corresponding cost defined definition denote depend derivatives deterministic difference discussion dynamic programming equation equivalent estimate Example exists exit fact finite fixed formula given gives Hence holds horizon implies inequality lateral Lemma limit linear Lipschitz Markov Markov diffusion Markov processes maximum measurable method minimizing Moreover nonlinear obtain operator optimal control partial differential equation particular positive principle probability proof prove Recall reference Remark replaced require respectively result satisfies Section Similarly smooth space step stochastic control stochastic differential equation subset sufficiently suitable supersolution Suppose term terminal Theorem 5.1 theory tion uniformly unique value function Verification viscosity solution viscosity subsolution yields