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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Results 1-3 of 55
Page 255
... formula I ( 8.5 ) : 1 L ( t , x , v ) = max b ( t , x ) · p − p · a ( t , x ) p - [ b ( t , · PERT By elementary calculus , ( 2.8 ) - - x ) p — v ⋅ p ] − q ( t , x ) . L ( t , x , v ) = { } ( b ( t , x ) — v ) · a ̄1 ( t , x ) ( b ( ...
... formula I ( 8.5 ) : 1 L ( t , x , v ) = max b ( t , x ) · p − p · a ( t , x ) p - [ b ( t , · PERT By elementary calculus , ( 2.8 ) - - x ) p — v ⋅ p ] − q ( t , x ) . L ( t , x , v ) = { } ( b ( t , x ) — v ) · a ̄1 ( t , x ) ( b ( ...
Page 389
... formula I ( 8.5 ) for H. The argument above shows that the mapping v →→ L , ( § , v ) is one - to- one and onto R ... formula in I ( 8.6 ) . The remaining formulas I ( 8.7b , c ) then follow by further differentiations . = Appendix B ...
... formula I ( 8.5 ) for H. The argument above shows that the mapping v →→ L , ( § , v ) is one - to- one and onto R ... formula in I ( 8.6 ) . The remaining formulas I ( 8.7b , c ) then follow by further differentiations . = Appendix B ...
Page 426
... formula , 128 , 391 Elliptic operators degenerate , 134 uniformly , 134 Euler equations , 35 , 42 , 45 exit time , 6 , 159 , 265 extremal , 35 Feedback control , 17 optimal , 17 Feller processes , 153 Feynman - Kac formula , 400 finite ...
... formula , 128 , 391 Elliptic operators degenerate , 134 uniformly , 134 Euler equations , 35 , 42 , 45 exit time , 6 , 159 , 265 extremal , 35 Feedback control , 17 optimal , 17 Feller processes , 153 Feynman - Kac formula , 400 finite ...
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