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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Results 1-3 of 90
Page 25
... consider problems in which V ( x ) > -∞o . This is true , in 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 O , rather than the more ...
... consider problems in which V ( x ) > -∞o . This is true , in 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 O , rather than the more ...
Page 70
... consider only the strict extrema of W – w . - Proof . Suppose that ( 4.2 ) holds at every strict minimum ( t , x ) Є Q of W - w with W ( t , x ) = w ( t , x ) . Let ( t , x ) E Q be a minimum ( not necessarily strict ) of Ww satisfying ...
... consider only the strict extrema of W – w . - Proof . Suppose that ( 4.2 ) holds at every strict minimum ( t , x ) Є Q of W - w with W ( t , x ) = w ( t , x ) . Let ( t , x ) E Q be a minimum ( not necessarily strict ) of Ww satisfying ...
Page 367
... consider the HJB partial differential equation ( 3.2 ) −Vt + H ( x , D ̧V , D2V ) = 0 , with H ( x , p , A ) as in IV ( 3.2 ) . As in Chapters IV and V , we consider ( 3.2 ) either in Qo with bounded terminal ( Cauchy ) data ( 3.3 ) V ...
... consider the HJB partial differential equation ( 3.2 ) −Vt + H ( x , D ̧V , D2V ) = 0 , with H ( x , p , A ) as in IV ( 3.2 ) . As in Chapters IV and V , we consider ( 3.2 ) either in Qo with bounded terminal ( Cauchy ) data ( 3.3 ) V ...
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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 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