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. |
From inside the book
Results 1-3 of 87
Page 6
... exit from a closed cylindrical region Q. Consider the following payoff functional J , which depends on states x ( s ) and controls u ( s ) for times s E [ t , T ) , where 7 is the smaller of t1 and the exit time of x ( s ) from the ...
... exit from a closed cylindrical region Q. Consider the following payoff functional J , which depends on states x ( s ) and controls u ( s ) for times s E [ t , T ) , where 7 is the smaller of t1 and the exit time of x ( s ) from the ...
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 ( T , x ( T ) ) Є Ə * 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 ( T , x ( T ) ) Є Ə * Q , where ( 2.6 ) T = Ə * Q = ( [ to , t1 ) ...
Contents
Viscosity Solutions | 53 |
Controlled Markov Diffusions in R | 157 |
SecondOrder Case | 213 |
Copyright | |
7 other sections not shown
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 convergence convex Corollary cylindrical region D₂V defined definition denote dynamic programming equation dynamic programming principle Dynkin formula Example exists exit finite first-order formulation given Hamilton-Jacobi equation Hence HJB equation holds implies inequality initial condition initial data lateral boundary Lebesgue left endpoint Lemma linear Lipschitz continuous Markov chain Markov control policy Markov processes maximum principle minimizing Moreover nonlinear obtain optimal control optimal control problems partial derivatives partial differential equation proof of Theorem prove R₁ reference probability system result satisfies second-order Section stochastic control stochastic differential equation Suppose t₁ Theorem 5.1 tion unique value function variations problem Verification Theorem viscosity solution viscosity subsolution viscosity supersolution yields