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 15
... exit from Q. Let us next consider the problem of control until the time 7 of exit from a closed cylindrical region Q ( class B , Section 3 ) . We first formulate appropriate boundary conditions for the dynamic programming equation ( 5.3 ) ...
... exit from Q. Let us next consider the problem of control until the time 7 of exit from a closed cylindrical region Q ( class B , Section 3 ) . We first formulate appropriate boundary conditions for the dynamic programming equation ( 5.3 ) ...
Page 159
... exit time of x ( s ) from O if exit occurs before time t1 , and t1 if x ( s ) E O for all s E [ t , t1 ) . We call 7 the exit time from the cylinder Q. One always has ( 7 , x ( 7 ) ) € 8 * Q , where ( 2.6 ) T = Ə * Q = ( [ to , t1 ) ...
... exit time of x ( s ) from O if exit occurs before time t1 , and t1 if x ( s ) E O for all s E [ t , t1 ) . We call 7 the exit time from the cylinder Q. One always has ( 7 , x ( 7 ) ) € 8 * Q , where ( 2.6 ) T = Ə * Q = ( [ to , t1 ) ...
Page 265
... exits from O by time t1 . This is of considerable importance in studying large deviations properties of nearly deterministic Markov dif- fusions ( Chapter VII ) . Let 0 denote the exit time of x ( s ) from O , and ( 5.1 ) where as ...
... exits from O by time t1 . This is of considerable importance in studying large deviations properties of nearly deterministic Markov dif- fusions ( Chapter VII ) . Let 0 denote the exit time of x ( s ) from O , and ( 5.1 ) where as ...
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