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 175
... replaced by -l , then the problem is to minimize -J . Thus -W must satisfy the equation corresponding to ( 5.21 ) , with min instead of max and replaced by -l . This has the form ( 5.8 ) . The value function V should be increasing on ...
... replaced by -l , then the problem is to minimize -J . Thus -W must satisfy the equation corresponding to ( 5.21 ) , with min instead of max and replaced by -l . This has the form ( 5.8 ) . The value function V should be increasing on ...
Page 363
... replaced by corresponding forward or backward finite difference quotients . Similarly , second - order partial derivatives are replaced by appropriate second - order finite - difference quotients ( Section 3. ) An important feature of ...
... replaced by corresponding forward or backward finite difference quotients . Similarly , second - order partial derivatives are replaced by appropriate second - order finite - difference quotients ( Section 3. ) An important feature of ...
Page 372
... replaced by △ Vh , just as in ( 3.9 ′ ) . If f¡ ( x , v ) ≥ 0 , then V1 is replaced by A + Vh , and if fi ( x , v ) < 0 it is replaced by AV . Similarly , V. , is replaced by A2Vh . For the mixed second - order partial i derivatives ...
... replaced by △ Vh , just as in ( 3.9 ′ ) . If f¡ ( x , v ) ≥ 0 , then V1 is replaced by A + Vh , and if fi ( x , v ) < 0 it is replaced by AV . Similarly , V. , is replaced by A2Vh . For the mixed second - order partial i derivatives ...
Contents
Viscosity Solutions | 53 |
Controlled Markov Diffusions in R | 157 |
SecondOrder Case | 213 |
Copyright | |
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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 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