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 86
Page 38
... Assumption ( 9.2a ) is the same as ( 8.3a ) and ( 9.2b ) is a stronger form of ( 8.3b ) . The remaining assumptions ( 9.2c - f ) will be used to obtain various bounds , for optimal controls and for the value function V. - Example 9.1 ...
... Assumption ( 9.2a ) is the same as ( 8.3a ) and ( 9.2b ) is a stronger form of ( 8.3b ) . The remaining assumptions ( 9.2c - f ) will be used to obtain various bounds , for optimal controls and for the value function V. - Example 9.1 ...
Page 76
... assumptions ( 16.1 ) , ( 16.3 ) , ( 16.4 ) are verified in the special case of LQRP and it is similar to condition I ( 9.2 ) . We postpone the statement of these assumptions to Section 16 ( See Theorem 16.1 . ) Theorem 7.1 . Suppose ...
... assumptions ( 16.1 ) , ( 16.3 ) , ( 16.4 ) are verified in the special case of LQRP and it is similar to condition I ( 9.2 ) . We postpone the statement of these assumptions to Section 16 ( See Theorem 16.1 . ) Theorem 7.1 . Suppose ...
Page 168
... assumptions are made : ( a ) U is compact ; ( b ) O is bounded with 20 a manifold of class C ( 3 ) ; ( 4.1 ) ( c ) for g = a , f , L , the function g and its partial derivatives 9t , 9 , 9xx , are continuous on Q × U , i , j = 1 ...
... assumptions are made : ( a ) U is compact ; ( b ) O is bounded with 20 a manifold of class C ( 3 ) ; ( 4.1 ) ( c ) for g = a , f , L , the function g and its partial derivatives 9t , 9 , 9xx , are continuous on Q × U , i , j = 1 ...
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 Cą(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