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 53
Page 55
... boundary and terminal con- ditions . This unique characterization of the value function is especially im- portant in ... condition satisfied by the value function . This issue of the boundary condition has been given a satisfactory ...
... boundary and terminal con- ditions . This unique characterization of the value function is especially im- portant in ... condition satisfied by the value function . This issue of the boundary condition has been given a satisfactory ...
Page 102
... boundary cost g ( t , x ) = 0. Note that V = g on the lateral boundary { -1,1 } × [ 0 , 1 ] and V and W do not agree ... condition satisfied by the value function when a state constraint is imposed . This condition plays an essential ...
... boundary cost g ( t , x ) = 0. Note that V = g on the lateral boundary { -1,1 } × [ 0 , 1 ] and V and W do not agree ... condition satisfied by the value function when a state constraint is imposed . This condition plays an essential ...
Page 106
... ) ) , W ( t , x ) − g ( t , x ) } ≤ 0 Ət - at every ( t , x ) Є arg max { ( W – w ) ( t , x ) | ( t , x ) = Q } [ to , t1 ) × 80 . ( b ) W is a viscosity supersolution of ( 106 II . Viscosity Solutions Discussion of boundary conditions.
... ) ) , W ( t , x ) − g ( t , x ) } ≤ 0 Ət - at every ( t , x ) Є arg max { ( W – w ) ( t , x ) | ( t , x ) = Q } [ to , t1 ) × 80 . ( b ) W is a viscosity supersolution of ( 106 II . Viscosity Solutions Discussion of boundary conditions.
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 C¹(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