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 137
... control pro- cesses u ( s ) which depend on the past in some more complicated way than through a Markov policy in ( 6.2 ) . This will be formalized later through the idea of admissible control system . In case of controlled diffusions ...
... control pro- cesses u ( s ) which depend on the past in some more complicated way than through a Markov policy in ( 6.2 ) . This will be formalized later through the idea of admissible control system . In case of controlled diffusions ...
Page 142
... admissible control system π . ( b ) If there exists an admissible system π * = ( N * , { F * } , P * , x * ( · ) , u * ( · ) ) such that u * ( s ) Є arg min [ A ° W ( s , x * ( s ) ) + L ( s , x * ( s ) , v ) ] for Lebesgue × P ...
... admissible control system π . ( b ) If there exists an admissible system π * = ( N * , { F * } , P * , x * ( · ) , u * ( · ) ) such that u * ( s ) Є arg min [ A ° W ( s , x * ( s ) ) + L ( s , x * ( s ) , v ) ] for Lebesgue × P ...
Page 151
... admissible control systems π ( not necessarily including all admissible π ) . Although one cannot generally expect V to be a classical solution of the dynamic programming equation , it is often possible to interpret V as a viscosity ...
... admissible control systems π ( not necessarily including all admissible π ) . Although one cannot generally expect V to be a classical solution of the dynamic programming equation , it is often possible to interpret V as a viscosity ...
Other editions - View all
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