## 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 86

Page 54

To

To

**define**this semigroup , we view a given function y as the terminal data to our optimal control problem . Then the value function with terminal data y is**defined**to be the evaluation of the semigroup at ¥ .Page 64

II.4

II.4

**Definition**In this section , we**define**the notion of viscosity solutions of the abstract dynamic programming equation ( 3.12 ) . This is a straightforward generalization of the original**definition**given by Crandall and Lions ( CL1 ) ...Page 141

( The space D was

( The space D was

**defined**in Section 6. ) In this section , we show that if W is a classical solution , then W ( t , x ) equals the minimum total expected cost among an appropriately**defined**class of admissible control systems .### 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