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 25
... particular , if L≥ 0 and g≥ 0 since then V ( x ) > 0. For simplicity , we consider in this section only the problem of control until exit from Ō , rather than the more general formulation in Section 3. In particular , we do not ...
... particular , if L≥ 0 and g≥ 0 since then V ( x ) > 0. For simplicity , we consider in this section only the problem of control until exit from Ō , rather than the more general formulation in Section 3. In particular , we do not ...
Page 95
... particular , we assume that f , L , are continuous functions and I ( 3.1 ) is satisfied . Theorem 10.1 . Suppose that U is bounded , Q = Qo = [ to , t1 ) × R " , U ( t , x ) = U ° ( t ) for every ( t , x ) E Qo . Moreover assume that f ...
... particular , we assume that f , L , are continuous functions and I ( 3.1 ) is satisfied . Theorem 10.1 . Suppose that U is bounded , Q = Qo = [ to , t1 ) × R " , U ( t , x ) = U ° ( t ) for every ( t , x ) E Qo . Moreover assume that f ...
Page 247
... particular , in ( 4.1 ) we may take V to be the value function of the stochastic control problem defined in Chapter IV . Then ( 4.1 ) becomes the dynamic programming equation IV ( 3.3 ) . If V € C ( Q ) satisfies ( 8.8 ) and the dynamic ...
... particular , in ( 4.1 ) we may take V to be the value function of the stochastic control problem defined in Chapter IV . Then ( 4.1 ) becomes the dynamic programming equation IV ( 3.3 ) . If V € C ( Q ) satisfies ( 8.8 ) and the dynamic ...
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