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 63
... operator . We also remark that the choice of D is not the largest possible one . A more careful analysis yields that the polynomial growth condition on the derivatives of w is not necessary . However D contains Co ( Qo ) and therefore ...
... operator . We also remark that the choice of D is not the largest possible one . A more careful analysis yields that the polynomial growth condition on the derivatives of w is not necessary . However D contains Co ( Qo ) and therefore ...
Page 70
... operator . A stability result for a gen- eral class of equations is also proved at the end of the section . See Lemma 6.3 . = Let Gt be a partial differential operator given by ( 4.3i ) , ' O be an open subset of R " and Σ = Ō . We also ...
... operator . A stability result for a gen- eral class of equations is also proved at the end of the section . See Lemma 6.3 . = Let Gt be a partial differential operator given by ( 4.3i ) , ' O be an open subset of R " and Σ = Ō . We also ...
Page 275
... operator of a Markov process x ( s ) , with state space Σ . Let ( t , x ) be a positive solution to ( 8.1 ) AÞ + q ( t , x ) Þ = 0 , ( t , x ) = [ to , t1 ] × Σ . We make the logarithmic transformation ( 8.2 ) V = ―- - log Þ . An ...
... operator of a Markov process x ( s ) , with state space Σ . Let ( t , x ) be a positive solution to ( 8.1 ) AÞ + q ( t , x ) Þ = 0 , ( t , x ) = [ to , t1 ] × Σ . We make the logarithmic transformation ( 8.2 ) V = ―- - log Þ . An ...
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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