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 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 ...
Page 53
... equation which we call the dynamic programing equation . For a determinis- tic optimal control problem , this ... programming equations in the classical or usual sense . Also there are many functions other than the value function which ...
... equation which we call the dynamic programing equation . For a determinis- tic optimal control problem , this ... programming equations in the classical or usual sense . Also there are many functions other than the value function which ...
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 ...
Contents
Viscosity Solutions | 53 |
Controlled Markov Diffusions in R | 157 |
SecondOrder Case | 213 |
Copyright | |
7 other sections not shown
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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