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 59
Page ix
... principle 9 1.5 Dynamic programming equation 11 1.6 Dynamic programming and Pontryagin's principle 18 1.7 Discounted cost with infinite horizon 23 1.8 Calculus of variations I 32 I.9 Calculus of variations II 37 I.10 Generalized ...
... principle 9 1.5 Dynamic programming equation 11 1.6 Dynamic programming and Pontryagin's principle 18 1.7 Discounted cost with infinite horizon 23 1.8 Calculus of variations I 32 I.9 Calculus of variations II 37 I.10 Generalized ...
Page 65
... principle : we say that Gt obeys the maximum principle if for every te [ to , til , and , in the domain of Gt , we have ( Gtø ) ( T ) ≤ ( Gt ¥ ) ( X ) , whenever I Є arg min { ( ø – ¥ ) ( x ) | x € Σ } ~ Σ ′ with p ( x ) = ( x ) . The ...
... principle : we say that Gt obeys the maximum principle if for every te [ to , til , and , in the domain of Gt , we have ( Gtø ) ( T ) ≤ ( Gt ¥ ) ( X ) , whenever I Є arg min { ( ø – ¥ ) ( x ) | x € Σ } ~ Σ ′ with p ( x ) = ( x ) . The ...
Page 214
... principle yields the fol- lowing : if W≤ V at the boundary , then this inequality holds everywhere . However the viscosity subsolutions and supersolutions are not necessar- ily semiconvex nor are they semiconcave . Therefore to use the ...
... principle yields the fol- lowing : if W≤ V at the boundary , then this inequality holds everywhere . However the viscosity subsolutions and supersolutions are not necessar- ily semiconvex nor are they semiconcave . Therefore to use the ...
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 continuous on Q convergence convex Corollary cylindrical region defined definition denote dynamic programming equation dynamic programming principle Dynkin formula Example exists exit finite first-order formulation Hamilton-Jacobi equation Hence HJB equation holds implies inequality initial data lateral boundary Lemma lim sup linear Lipschitz continuous Markov chain Markov control policy Markov processes maximum principle minimizing Moreover nonlinear obtain optimal control optimal control problem partial derivatives partial differential equation proof of Theorem prove result satisfies second-order Section semigroup stochastic differential equation Suppose t₁ test function Theorem 5.1 uniformly continuous unique value function variations problem Verification Theorem viscosity solution viscosity subsolution viscosity supersolution yields