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 136
... Markov chain are given , as in Section 4 , Example ( a ) . If control u ( s ) is used at time s , the jumping rates are p ( s , x , y , u ( s ) ) . Example 6.2 . ( Controlled Markov diffusion ) . In this case we suppose that x ( s ) ...
... Markov chain are given , as in Section 4 , Example ( a ) . If control u ( s ) is used at time s , the jumping rates are p ( s , x , y , u ( s ) ) . Example 6.2 . ( Controlled Markov diffusion ) . In this case we suppose that x ( s ) ...
Page 157
Wendell Helms Fleming, H. Mete Soner. IV Controlled Markov Diffusions in Rn IV.1 Introduction This chapter is concerned with the control of Markov diffusion processes in n - dimensional R " . The dynamics of the process r ( s ) being ...
Wendell Helms Fleming, H. Mete Soner. IV Controlled Markov Diffusions in Rn IV.1 Introduction This chapter is concerned with the control of Markov diffusion processes in n - dimensional R " . The dynamics of the process r ( s ) being ...
Page 426
... diffusion processes , 161 diffusion processes with infi- nite horizon , 171 controlled Markov processes , 139 , 223 dynamic programming principle abstract , 60 controlled Markov processes , 138 , 219 deterministic , 11 diffusion ...
... diffusion processes , 161 diffusion processes with infi- nite horizon , 171 controlled Markov processes , 139 , 223 dynamic programming principle abstract , 60 controlled Markov processes , 138 , 219 deterministic , 11 diffusion ...
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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