## 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 15

Control until

Control until

**exit**from Q. Let us next consider the problem of control until the time t of**exit**from a closed cylindrical region Q ( class B , Section 3 ) . We first formulate appropriate boundary conditions for the dynamic programming ...Page 159

However , instead of controlling on the fixed interval [ t , tı ) we control up to the smaller of tị and the

However , instead of controlling on the fixed interval [ t , tı ) we control up to the smaller of tị and the

**exit**time of x ( s ) from a given open set O CR ” . We assume that either O = R " or that all is a compact ( n − 1 ) ...Page 265

VI.5 The

VI.5 The

**exit**problem We again consider a solution x ( s ) to the stochastic differential equation ( 2.1 ) on x ( t , tı ) with z ( t ) ... The first quantity which we consider is the probability that x ( 3 )**exits**from O by time tı .### 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