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 313
... Soner [ DIS ] studied the large deviations problem of a queueing system , and asymptotic expansions for jump Markov processes were derived by Fleming and Soner [ FSo ] . The application to homogenization is due to Evans [ E3 ] . Evans ...
... Soner [ DIS ] studied the large deviations problem of a queueing system , and asymptotic expansions for jump Markov processes were derived by Fleming and Soner [ FSo ] . The application to homogenization is due to Evans [ E3 ] . Evans ...
Page 362
... Soner and Shreve proved the twice differentiability of the value function under two sets of assumptions , ( 4.18i ) and ( 4.18ii ) [ SSh1-2 ] . One dimensional convex problem received much attention in the early 1980's . Karatzas [ K1 ] ...
... Soner and Shreve proved the twice differentiability of the value function under two sets of assumptions , ( 4.18i ) and ( 4.18ii ) [ SSh1-2 ] . One dimensional convex problem received much attention in the early 1980's . Karatzas [ K1 ] ...
Page 422
... Soner , Optimal investment and consump- tion with transaction costs , preprint . [ SSX ] S. E. Shreve , H. M. Soner and G.-L. Xu , Optimal investment and consumption with two bonds and transaction costs , Mathematical Finance , 1 ( 1991 ) ...
... Soner , Optimal investment and consump- tion with transaction costs , preprint . [ SSX ] S. E. Shreve , H. M. Soner and G.-L. Xu , Optimal investment and consumption with two bonds and transaction costs , Mathematical Finance , 1 ( 1991 ) ...
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