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 170
... assume that σ ( t , x ) is a nonsingular n x n matrix ( which does not depend on v ) . Moreover , we assume that there exists C such that , for all ( t , x ) Є Qo ' ( 4.9 ) lo - 1 ( t , x ) | ≤ C. Assumption ( 4.9 ) implies ( 3.5 ) ...
... assume that σ ( t , x ) is a nonsingular n x n matrix ( which does not depend on v ) . Moreover , we assume that there exists C such that , for all ( t , x ) Є Qo ' ( 4.9 ) lo - 1 ( t , x ) | ≤ C. Assumption ( 4.9 ) implies ( 3.5 ) ...
Page 185
... Assume ( 6.1 ) - ( 6.3 ) . Then V is continuous on Qo and property ( DP ) holds . Moreover , V = V for every reference probability system v . Proof . Step 1. Assume that ( 3.5 ) and ( 4.5 ) hold . Then the conclusions of Theorem 7.1 ...
... Assume ( 6.1 ) - ( 6.3 ) . Then V is continuous on Qo and property ( DP ) holds . Moreover , V = V for every reference probability system v . Proof . Step 1. Assume that ( 3.5 ) and ( 4.5 ) hold . Then the conclusions of Theorem 7.1 ...
Page 299
... assume the Lipschitz continuity of V , and relax ( 8.1 ) to hold only locally . However we do not assume that H is related to a calculus of variations problem . We assume that for every R > 0 there are a constant KR and a nondecreasing ...
... assume the Lipschitz continuity of V , and relax ( 8.1 ) to hold only locally . However we do not assume that H is related to a calculus of variations problem . We assume that for every R > 0 there are a constant KR and a nondecreasing ...
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