## 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 259

VI.3 Locally optimal Markov policies We are interested in solutions to ( 2.4 ) which are

VI.3 Locally optimal Markov policies We are interested in solutions to ( 2.4 ) which are

**positive**in Q but may be zero at some points of Ə * Q . If $ is continuous at ( t , x ) E * Q and Q ( t , x ) = 0 , then we assign V = -log ...Page 262

We first condition on an event x ( ti ) e B , where B is a compact set of

We first condition on an event x ( ti ) e B , where B is a compact set of

**positive**Lebesgue measure . Then we consider " ied down " diffusions which result by requiring that x ( tı ) = x1 , with qi e Rn given . In either case , 262 VI .Page 371

As in the one - dimensional case , let fit and fi denote the

As in the one - dimensional case , let fit and fi denote the

**positive**and negative parts of fi , i = 1 , ... , n . The matrices a ( z , v ) = ( aij ( x , v ) ) , i , j = 1 , ... , n , are nonnegative definite . Hence Qii > 0.### 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