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 168
Wendell Helms Fleming, H. Mete Soner. without proof , some results of this kind . These results are proved by meth- ods in the theory of second - order nonlinear parabolic partial differential equations . In the first result which we ...
Wendell Helms Fleming, H. Mete Soner. without proof , some results of this kind . These results are proved by meth- ods in the theory of second - order nonlinear parabolic partial differential equations . In the first result which we ...
Page 247
... result is an immediate consequence of Theorem 8.1 . Corollary 8.1 . ( Uniqueness ) . Assume ( 8.1 ) . Then there is at most one viscosity solution V of ( 4.1 ) in Q satisfying the boundary and terminal conditions ( 8.8a ) ( 8.8b ) V ( t ...
... result is an immediate consequence of Theorem 8.1 . Corollary 8.1 . ( Uniqueness ) . Assume ( 8.1 ) . Then there is at most one viscosity solution V of ( 4.1 ) in Q satisfying the boundary and terminal conditions ( 8.8a ) ( 8.8b ) V ( t ...
Page 403
Wendell Helms Fleming, H. Mete Soner. Appendix E A Result of Alexandrov The purpose of this appendix is to prove that semiconvex functions are almost everywhere twice differentiable . This is a classical result due to Alexandrov [ A1 ] ...
Wendell Helms Fleming, H. Mete Soner. Appendix E A Result of Alexandrov The purpose of this appendix is to prove that semiconvex functions are almost everywhere twice differentiable . This is a classical result due to Alexandrov [ A1 ] ...
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