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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... horizon Infinite time horizon 140 145 III.10 Viscosity solutions 151 III.11 Historical remarks 155 IV Controlled Markov Diffusions in R " 157 IV.1 Introduction 157 IV.2 Finite time horizon problem 158 IV.3 Hamilton - Jacobi - Bellman ...
... horizon Infinite time horizon 140 145 III.10 Viscosity solutions 151 III.11 Historical remarks 155 IV Controlled Markov Diffusions in R " 157 IV.1 Introduction 157 IV.2 Finite time horizon problem 158 IV.3 Hamilton - Jacobi - Bellman ...
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... horizon In this section we study a class of problems with infinite time horizon ( t1 = ∞ ) . With the notation of Section 3 , the payoff functional is ( 7.1 ) J ( t , x ; u ) = [ " L ( s , x ( 8 ) , u ( 8 ) ) ds + g ( 7 , 2 ( 7 ) ) Xr ...
... horizon In this section we study a class of problems with infinite time horizon ( t1 = ∞ ) . With the notation of Section 3 , the payoff functional is ( 7.1 ) J ( t , x ; u ) = [ " L ( s , x ( 8 ) , u ( 8 ) ) ds + g ( 7 , 2 ( 7 ) ) Xr ...
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... horizon discounted cost control problem . Consider the problem of minimizing ( 7.11 ) J = E2 E. [ ° е e ̄ß3 L ( x ( s ) , u ( s ) ) ds and introduce ( again formally ) the value function ( 7.12 ) V ( x ) = inf J ( x ; control ) , C1 ...
... horizon discounted cost control problem . Consider the problem of minimizing ( 7.11 ) J = E2 E. [ ° е e ̄ß3 L ( x ( s ) , u ( s ) ) ds and introduce ( again formally ) the value function ( 7.12 ) V ( x ) = inf J ( x ; control ) , C1 ...
Contents
Viscosity Solutions | 53 |
Controlled Markov Diffusions in R | 157 |
SecondOrder Case | 213 |
Copyright | |
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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