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 161
... reference probability systems admitted . One such restriction would be to require that F , is the o - algebra generated by the brownian motion w ( · ) , instead of assuming ( as we have done ) only that w ( ) is F. - adapted . In the ...
... reference probability systems admitted . One such restriction would be to require that F , is the o - algebra generated by the brownian motion w ( · ) , instead of assuming ( as we have done ) only that w ( ) is F. - adapted . In the ...
Page 183
... reference probability system v , a discrete- time Markov control policy u defines u ( · ) € At , and solution x ( · ) to ( 2.1 ) , such that ( 7.2 ) -- - u ( s ) = u ( x ( s ; ) ) if s E Ij , j = 0 , 1 , ... , M – 1 . - ū This is done ...
... reference probability system v , a discrete- time Markov control policy u defines u ( · ) € At , and solution x ( · ) to ( 2.1 ) , such that ( 7.2 ) -- - u ( s ) = u ( x ( s ; ) ) if s E Ij , j = 0 , 1 , ... , M – 1 . - ū This is done ...
Page 186
... reference probability system v = ( N , { F } , P , w ) and u ( ) E Atv , the product space construction in the proof of Lemma 6.3 provides a brownian motion w1 independent of w and reference probability system such that u ( · ) E Atu ...
... reference probability system v = ( N , { F } , P , w ) and u ( ) E Atv , the product space construction in the proof of Lemma 6.3 provides a brownian motion w1 independent of w and reference probability system such that u ( · ) E Atu ...
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 Cą(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