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 34
... partial derivatives of L and H also hold : ( 8.7 ) ( a ) Ht = -Lt , Hx = −Lx ; ( b ) Hpp = ( Lvv ) −1 ; ( c ) Htp = LtvHpp , Hr 、 p = L ̧vHpp . In ( 8.7 ) the partial derivatives of L and H are evaluated at ( t , x , v ) and ( t , x ...
... partial derivatives of L and H also hold : ( 8.7 ) ( a ) Ht = -Lt , Hx = −Lx ; ( b ) Hpp = ( Lvv ) −1 ; ( c ) Htp = LtvHpp , Hr 、 p = L ̧vHpp . In ( 8.7 ) the partial derivatives of L and H are evaluated at ( t , x , v ) and ( t , x ...
Page 168
... partial differential equations . In the first result which we cite the ... derivatives 9t , 9 , 9 , are continuous on Q × U , i , j = 1 , ... , n ; ( d ) ... partial differential equation of the form ( 4.2 ) is called semilinear , since D2V ...
... partial differential equations . In the first result which we cite the ... derivatives 9t , 9 , 9 , are continuous on Q × U , i , j = 1 , ... , n ; ( d ) ... partial differential equation of the form ( 4.2 ) is called semilinear , since D2V ...
Page 198
... derivatives of V are defined as follows [ Zi ] . Suppose that there exists i E Loc ( Qo ) such that ( 10.1 ) E Voz.drdt for all € Co ° ( Qo ) . V1odxdt = - LV42 , Qo Then ; is called a generalized first - order partial derivative of V ...
... derivatives of V are defined as follows [ Zi ] . Suppose that there exists i E Loc ( Qo ) such that ( 10.1 ) E Voz.drdt for all € Co ° ( Qo ) . V1odxdt = - LV42 , Qo Then ; is called a generalized first - order partial derivative of V ...
Contents
Viscosity Solutions | 53 |
Controlled Markov Diffusions in R | 157 |
SecondOrder Case | 213 |
Copyright | |
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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