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 240
... approximations In this section we introduce an approximation procedure of Lasry and Li- ons [ LL ] and Jensen [ J ] . ( See Jensen - Lions - Souganidis [ JLS ] for more in- formation on this approximation ) . These approximations are ...
... approximations In this section we introduce an approximation procedure of Lasry and Li- ons [ LL ] and Jensen [ J ] . ( See Jensen - Lions - Souganidis [ JLS ] for more in- formation on this approximation ) . These approximations are ...
Page 366
... approximating sequence is monotone nondecreasing : WmWm + 1 . The method of approximation in policy space proceeds as follows . Let uo be an initial choice of stationary Markov control policy . Define Wm . successively for m = 0 , 1 , 2 ...
... approximating sequence is monotone nondecreasing : WmWm + 1 . The method of approximation in policy space proceeds as follows . Let uo be an initial choice of stationary Markov control policy . Define Wm . successively for m = 0 , 1 , 2 ...
Page 374
... approximation in policy space . The discount factor λ = exp ( -ẞh ) in ( 3.19 ) is nearly 1 for small h , and the contraction in ( 2.10 ) is weak . For small h , the successive approximations to Vh through value iteration tend to ...
... approximation in policy space . The discount factor λ = exp ( -ẞh ) in ( 3.19 ) is nearly 1 for small h , and the contraction in ( 2.10 ) is weak . For small h , the successive approximations to Vh through value iteration tend to ...
Contents
Viscosity Solutions | 53 |
Controlled Markov Diffusions in R | 157 |
SecondOrder Case | 213 |
Copyright | |
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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 convergence convex Corollary cylindrical region D₂V defined definition denote dynamic programming equation dynamic programming principle Dynkin formula Example exists exit finite first-order formulation given Hamilton-Jacobi equation Hence HJB equation holds implies inequality initial condition initial data lateral boundary Lebesgue left endpoint Lemma linear Lipschitz continuous Markov chain Markov control policy Markov processes maximum principle minimizing Moreover nonlinear obtain optimal control optimal control problems partial derivatives partial differential equation proof of Theorem prove R₁ reference probability system result satisfies second-order Section stochastic control stochastic differential equation Suppose t₁ Theorem 5.1 tion unique value function variations problem Verification Theorem viscosity solution viscosity subsolution viscosity supersolution yields