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 132
... Markov process . The Fundamental Theorem of Calculus gives Grp ( x ) = f ( t , x ) · Do ( x ) . For the ... Markov chain parameters . Let z ( s ) be a finite- state Markov chain , with state space a finite set Z. We regard z ...
... Markov process . The Fundamental Theorem of Calculus gives Grp ( x ) = f ( t , x ) · Do ( x ) . For the ... Markov chain parameters . Let z ( s ) be a finite- state Markov chain , with state space a finite set Z. We regard z ...
Page 136
... process u ( s ) , called a control process . The control process has values u ( s ) € U , where U is a complete separable metric space . We refer to Σ as the state space and U as the control space . Example 6.1 . ( Controlled Markov chain ) ...
... process u ( s ) , called a control process . The control process has values u ( s ) € U , where U is a complete separable metric space . We refer to Σ as the state space and U as the control space . Example 6.1 . ( Controlled Markov chain ) ...
Page 278
... Markov diffusions . For technical simplicity , let us again consider only finite - state Markov chains . Let x ( s ) be an irreducible , time - homogeneous Markov chain under probability measure Po , with state space Σ . Given B C Σ ...
... Markov diffusions . For technical simplicity , let us again consider only finite - state Markov chains . Let x ( s ) be an irreducible , time - homogeneous Markov chain under probability measure Po , with state space Σ . Given B C Σ ...
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 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