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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Page xiv
... respectively . We denote the gradient vector and matrix of second - order partial deriva- tives of by D ¢ = ( a , ... , an ) , D2 = ( $ x , x , ) , i , j = 1 , ... , n . Sometimes these are denoted instead by Or , Paz , respectively ...
... respectively . We denote the gradient vector and matrix of second - order partial deriva- tives of by D ¢ = ( a , ... , an ) , D2 = ( $ x , x , ) , i , j = 1 , ... , n . Sometimes these are denoted instead by Or , Paz , respectively ...
Page 3
... respectively , the inventory and control vectors at times , and the demand vector . The rate of change of the inventory x ( s ) € R ” is ( 2.1 ) d -x ( s ) = u ( s ) – d . ds – Let us consider the production planning problem on a given ...
... respectively , the inventory and control vectors at times , and the demand vector . The rate of change of the inventory x ( s ) € R ” is ( 2.1 ) d -x ( s ) = u ( s ) – d . ds – Let us consider the production planning problem on a given ...
Page 339
... respectively . Then x ( s ) and y ( s ) change according to ( 6.1i ) ( 6.1ii ) dx ( s ) = [ ax ( s ) − c ( s ) ] ds ... respectively . Here we should warn the reader that in this section the con- sumption rate c ( s ) is a control ...
... respectively . Then x ( s ) and y ( s ) change according to ( 6.1i ) ( 6.1ii ) dx ( s ) = [ ax ( s ) − c ( s ) ] ds ... respectively . Here we should warn the reader that in this section the con- sumption rate c ( s ) is a control ...
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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 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