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 125
... Markov diffusion processes , the dynamic programming equation becomes a second - order nonlinear partial differential equation . Controlled Markov diffusions will be considered in much more detail in Chapters IV and V. When there is a ...
... Markov diffusion processes , the dynamic programming equation becomes a second - order nonlinear partial differential equation . Controlled Markov diffusions will be considered in much more detail in Chapters IV and V. When there is a ...
Page 136
... Markov , or which are Markov on a higher dimensional state space . For a treatment of such situations and applications in communications engineering , see [ Ku2 ] . III.6 Controlled Markov processes We now consider problems in which the ...
... Markov , or which are Markov on a higher dimensional state space . For a treatment of such situations and applications in communications engineering , see [ Ku2 ] . III.6 Controlled Markov processes We now consider problems in which the ...
Page 137
... Markov process . Discontinuous Markov policies u must often be admitted , in order to obtain a policy u * which minimizes an expected cost criterion J of the type ( 6.5 ) below . This introduces additional mathematical complications ...
... Markov process . Discontinuous Markov policies u must often be admitted , in order to obtain a policy u * which minimizes an expected cost criterion J of the type ( 6.5 ) below . This introduces additional mathematical complications ...
Contents
Viscosity Solutions | 53 |
Controlled Markov Diffusions in R | 157 |
SecondOrder Case | 213 |
Copyright | |
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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 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