## 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

Results 1-3 of 92

Page vii

The fundamental equation of dynamic programming is a nonlinear evolution equation for the value function . For controlled Markov diffusion processes on n - dimensional euclidean space , the

The fundamental equation of dynamic programming is a nonlinear evolution equation for the value function . For controlled Markov diffusion processes on n - dimensional euclidean space , the

**dynamic programming equation**becomes a ...Page 53

When the value function is smooth enough , it solves a nonlinear equation which we call the

When the value function is smooth enough , it solves a nonlinear equation which we call the

**dynamic programing equation**. For a deterministic optimal control problem , this derivation is given in Section 1.5 . A similar computation for ...Page 54

To capture this variety in

To capture this variety in

**dynamic programing equations**we give an abstract discussion of viscosity solutions in Section 4. In this abstract formulation the dynamic programming operator is viewed as the infinitesimal generator of a two ...### What people are saying - Write a review

We haven't found any reviews in the usual places.

### 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