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 ] ...
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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 brownian motion C₁ Cą(Q calculus of variations Chapter classical solution consider continuous on Q controlled Markov diffusion convergence convex Corollary D₂V defined definition denote deterministic dynamic programming equation dynamic programming principle Dynkin formula Example exists exit finite formula Hence HJB equation holds implies inequality initial data lateral boundary Lebesgue Lemma lim sup linear Lipschitz continuous Markov chain Markov control policy Markov processes maximum principle minimizing Moreover nonlinear obtain optimal control optimal Markov control partial derivatives partial differential equation proof of Theorem prove reference probability system Remark result satisfies second-order Section semiconvex stochastic control stochastic differential equation Suppose t₁ Theorem 5.1 uniformly continuous unique value function Verification Theorem viscosity solution viscosity subsolution viscosity supersolution yields