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 75
Page vii
... Chapter I , and to the corresponding theory of viscosity solutions in Chapter II . A rather elementary introduc- tion to dynamic programming for controlled Markov processes is provided in Chapter III . This is followed by the more ...
... Chapter I , and to the corresponding theory of viscosity solutions in Chapter II . A rather elementary introduc- tion to dynamic programming for controlled Markov processes is provided in Chapter III . This is followed by the more ...
Page 55
... ( Chapter VII ) and in the numerical analysis of the control problems ( Chapter IX ) . To characterize a viscosity solution uniquely we need to specify the so- lution at the terminal time and at the boundary of the state space . In some ...
... ( Chapter VII ) and in the numerical analysis of the control problems ( Chapter IX ) . To characterize a viscosity solution uniquely we need to specify the so- lution at the terminal time and at the boundary of the state space . In some ...
Page 213
... chapter we study the exit time control of a Markov diffusion pro- cess as formulated in Section IV.2 . With the exception of the last section , we assume that the state space is a bounded finite - dimensional set . The main purpose of ...
... chapter we study the exit time control of a Markov diffusion pro- cess as formulated in Section IV.2 . With the exception of the last section , we assume that the state space is a bounded finite - dimensional set . The main purpose of ...
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 control assume assumptions boundary condition boundary data bounded c₁ C¹(Q calculus of variations Chapter classical solution consider constant convergence convex Corollary cylindrical region D₂V defined definition denote dynamic programming equation dynamic programming principle Dynkin formula Example exists exit finite first-order formulation given Hamilton-Jacobi equation Hence HJB equation holds implies inequality initial condition initial data lateral boundary Lebesgue left endpoint Lemma linear Lipschitz continuous Markov chain Markov control policy Markov processes maximum principle minimizing Moreover nonlinear obtain optimal control optimal control problems partial derivatives partial differential equation proof of Theorem prove R₁ reference probability system result satisfies second-order Section stochastic control stochastic differential equation Suppose t₁ Theorem 5.1 tion unique value function variations problem Verification Theorem viscosity solution viscosity subsolution viscosity supersolution yields