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 35
Page 16
... corollary to Theorem 5.2 . Corollary 5.1 . A control u * ( ) satisfies the optimality condition ( 5.7 ) if x * ( · ) is a solution to the differential inclusion ( 5.22 ) . Feedback controls ( Markov control policies ) . Corollary 5.1 is ...
... corollary to Theorem 5.2 . Corollary 5.1 . A control u * ( ) satisfies the optimality condition ( 5.7 ) if x * ( · ) is a solution to the differential inclusion ( 5.22 ) . Feedback controls ( Markov control policies ) . Corollary 5.1 is ...
Page 93
... Corollary 8.2 yield comparison and uniqueness re- sults for Lipschitz continuous sub- and supersolutions . Indeed , in view of Corollary 8.2 any Lipschitz continuous sub- or supersolution of the dynamic programming equation of the ...
... Corollary 8.2 yield comparison and uniqueness re- sults for Lipschitz continuous sub- and supersolutions . Indeed , in view of Corollary 8.2 any Lipschitz continuous sub- or supersolution of the dynamic programming equation of the ...
Page 166
... Corollary 3.1 . If there exists u " EL such that ( 3.15 ) u * ( s , y ) = arg min [ ƒ ( s , y , v ) · D ̧W ( s , y ) + tra ( s , y , v ) D2W ( s , y ) + L ( s , y , v ) ] for all ( s , y ) E Q , then W ( t , x ) = J ( t , x ; u * ) for ...
... Corollary 3.1 . If there exists u " EL such that ( 3.15 ) u * ( s , y ) = arg min [ ƒ ( s , y , v ) · D ̧W ( s , y ) + tra ( s , y , v ) D2W ( s , y ) + L ( s , y , v ) ] for all ( s , y ) E Q , then W ( t , x ) = J ( t , x ; u * ) for ...
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