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 75
Page xiv
... denote the gradient vector and matrix of second - order partial deriva- tives of by D ˘ = ( a , ... , an ) , D2 ... denote intervals of IR1 , respectively , closed and half - open to the right , by Given to < ti Qo = [ to , t1 ) x R ...
... denote the gradient vector and matrix of second - order partial deriva- tives of by D ˘ = ( a , ... , an ) , D2 ... denote intervals of IR1 , respectively , closed and half - open to the right , by Given to < ti Qo = [ to , t1 ) x R ...
Page 126
... denote the Borel σ - algebra , namely , the least σ - algebra containing all open subsets of Σ . = = .... = Elements of the state space Σ will be denoted by x , y , Let Io C R1 be an interval half open to the right , and let Ĩo be the ...
... denote the Borel σ - algebra , namely , the least σ - algebra containing all open subsets of Σ . = = .... = Elements of the state space Σ will be denoted by x , y , Let Io C R1 be an interval half open to the right , and let Ĩo be the ...
Page 371
... denote the positive and negative parts of fi , i = 1 , ... , n . The matrices a ( x , v ) ( aij ( x , v ) ) , i , j = 1 , ... , n , are nonnegative definite . Hence a ≥0 . For j ‡ i , let aj , aj , denote the positive and negative ...
... denote the positive and negative parts of fi , i = 1 , ... , n . The matrices a ( x , v ) ( aij ( x , v ) ) , i , j = 1 , ... , n , are nonnegative definite . Hence a ≥0 . For j ‡ i , let aj , aj , denote the positive and negative ...
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