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 34
Page 186
... brownian motion independent of w ( · ) . Consider any reference probability system μ = ( N , { F. } , P , w , w1 ) and u ( · ) € Atμ . Let în ( s ) be the solution to dxn = fn ( 8 , xn ( 3 ) , u ( s ) ) ds + On ( 8 , în ( 3 ) , u ( s ) ...
... brownian motion independent of w ( · ) . Consider any reference probability system μ = ( N , { F. } , P , w , w1 ) and u ( · ) € Atμ . Let în ( s ) be the solution to dxn = fn ( 8 , xn ( 3 ) , u ( s ) ) ds + On ( 8 , în ( 3 ) , u ( s ) ...
Page 205
... brownian motion and the control process u ( · ) is R - valued ( thus U = R " . ) The problem is : given initial data x ( t ) x , minimize ( 11.2 ) J ( t , x ; u ) = Etz { [ " L ( s , x ( s ) , u ( s ) ) ds + 4 ( x ( t ) ( x ( t ) ...
... brownian motion and the control process u ( · ) is R - valued ( thus U = R " . ) The problem is : given initial data x ( t ) x , minimize ( 11.2 ) J ( t , x ; u ) = Etz { [ " L ( s , x ( s ) , u ( s ) ) ds + 4 ( x ( t ) ( x ( t ) ...
Page 362
... brownian motions . Soner and Shreve proved the regularity of the interface and then constructed the optimal process as the reflected Brownian motion in [ SSh1- 2 ] . Williams - Chow - Menaldi [ WCM ] also proved partial regularity ...
... brownian motions . Soner and Shreve proved the regularity of the interface and then constructed the optimal process as the reflected Brownian motion in [ SSh1- 2 ] . Williams - Chow - Menaldi [ WCM ] also proved partial regularity ...
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