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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Page 2
... partial differential equation in the usual ( " classical " ) sense . However , in such cases V can be interpreted as a viscosity solution , as will be explained in Chapter II . Closely related to dynamic programming is the idea of ...
... partial differential equation in the usual ( " classical " ) sense . However , in such cases V can be interpreted as a viscosity solution , as will be explained in Chapter II . Closely related to dynamic programming is the idea of ...
Page 34
... partial derivatives of L and H are evaluated at ( t , x , v ) and ( t , x , p ) , where v and p are related by the Legendre transformation ( 8.6 ) . For a calculus of variations problem the adjoint differential ... equation for a calculus of ...
... partial derivatives of L and H are evaluated at ( t , x , v ) and ( t , x , p ) , where v and p are related by the Legendre transformation ( 8.6 ) . For a calculus of variations problem the adjoint differential ... equation for a calculus of ...
Page 54
Wendell Helms Fleming, H. Mete Soner. equation , and a piecewise deterministic process gives rise to a system of first - order partial differential equations . To capture this variety in dynamic programing equations we give an abstract ...
Wendell Helms Fleming, H. Mete Soner. equation , and a piecewise deterministic process gives rise to a system of first - order partial differential equations . To capture this variety in dynamic programing equations we give an abstract ...
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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 Cą(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