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 17
... control policy . Such a function u will also be called in later chapters a Markov control policy . Consider the differential equation ( 5.23 ) 8 d -x ( s ) = f ( s , x ( 8 ) , u ( s , x ( s ) ) ) , s E [ t , t1 ] . ds If ( 5.23 ) with ...
... control policy . Such a function u will also be called in later chapters a Markov control policy . Consider the differential equation ( 5.23 ) 8 d -x ( s ) = f ( s , x ( 8 ) , u ( s , x ( s ) ) ) , s E [ t , t1 ] . ds If ( 5.23 ) with ...
Page 137
... Markov control policy u * satisfying ( 7.7 ) below is a natural candidate for an optimal policy . However , in some cases there is no Markov process cor- responding to u * . This difficulty is encountered for degenerate controlled Markov ...
... Markov control policy u * satisfying ( 7.7 ) below is a natural candidate for an optimal policy . However , in some cases there is no Markov process cor- responding to u * . This difficulty is encountered for degenerate controlled Markov ...
Page 183
... Markov control policy , relative to this partition . Given initial data ( t , x ) and any reference probability system v , a discrete- time Markov control policy u defines u ( · ) € At , and solution x ( · ) to ( 2.1 ) , such that ( 7.2 ) ...
... Markov control policy , relative to this partition . Given initial data ( t , x ) and any reference probability system v , a discrete- time Markov control policy u defines u ( · ) € At , and solution x ( · ) to ( 2.1 ) , such that ( 7.2 ) ...
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