## 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. |

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Page 125

III Optimal Control of

III Optimal Control of

**Markov**Processes : Classical Solutions III.1 Introduction The purpose of this chapter is to give a concise , nontechnical introduction to optimal stochastic control for**Markov**processes .Page 136

In other applications a diffusion limit is obtained for processes which are not

In other applications a diffusion limit is obtained for processes which are not

**Markov**, or which are**Markov**on a higher dimensional state space . For a treatment of such situations and applications in communications engineering ...Page 275

VI.8 Logarithmic transformations for

VI.8 Logarithmic transformations for

**Markov**processes In this section we shall outline how to extend some of the results described in Sections 2–5 for**Markov**diffusion processes to other classes of**Markov**processes .### 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