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 187
... Step 3. Given f , o , L satisfying ( 6.1b ) , ( 6.1c ) and ( 6.3 ) , let ƒ , = apf , Lp a , L as in Section 6. By Step 2 , the corresponding value function V , is con- tinuous and property ( DP ) holds for the problem determined by fp ...
... Step 3. Given f , o , L satisfying ( 6.1b ) , ( 6.1c ) and ( 6.3 ) , let ƒ , = apf , Lp a , L as in Section 6. By Step 2 , the corresponding value function V , is con- tinuous and property ( DP ) holds for the problem determined by fp ...
Page 367
... step h > 0 and a spatial step 8 > 0 , which will be related in such a way that inequality ( 3.7 ) below holds . The approximating con- trolled discrete - time Markov chain has as state space the one - dimensional lattice ( 3.4 ) Let Σh ...
... step h > 0 and a spatial step 8 > 0 , which will be related in such a way that inequality ( 3.7 ) below holds . The approximating con- trolled discrete - time Markov chain has as state space the one - dimensional lattice ( 3.4 ) Let Σh ...
Page 370
... step transition probabilities must be changed at boundary points of Σh . Let us suppose that ( 3.14 ) Σ * = { z Ε Σ : [ z ] < Bn } , where Bh represents some finite " cutoff " parameter ( Bh Є Σb . ) We need to redefine the controlled ...
... step transition probabilities must be changed at boundary points of Σh . Let us suppose that ( 3.14 ) Σ * = { z Ε Σ : [ z ] < Bn } , where Bh represents some finite " cutoff " parameter ( Bh Є Σb . ) We need to redefine the controlled ...
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