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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Results 1-3 of 88
Page 169
... bounded on Qo × U , i , j = 1 , ... , n ; ( d ) & Є C2 ( R ” ) . Theorem 4.2 . Let Q = Qo . If assumptions ( 3.5 ) ... bounded on Qo , whereas E C1 ( Q 。× U ) with e , bounded ; ( d ) Le C1 × U ) , and L , L , satisfy a polynomial growth ...
... bounded on Qo × U , i , j = 1 , ... , n ; ( d ) & Є C2 ( R ” ) . Theorem 4.2 . Let Q = Qo . If assumptions ( 3.5 ) ... bounded on Qo , whereas E C1 ( Q 。× U ) with e , bounded ; ( d ) Le C1 × U ) , and L , L , satisfy a polynomial growth ...
Page 257
... bounded . Moreover , u * = -D & V is an optimal control policy , with u * € L. The unique bounded solution to ( 2.14 ) with ( t1 , x ) = exp ( − ( x ) ) is ☀ = exp ( −V ) . Remark 2.1 . The following is an alternate way to introduce ...
... bounded . Moreover , u * = -D & V is an optimal control policy , with u * € L. The unique bounded solution to ( 2.14 ) with ( t1 , x ) = exp ( − ( x ) ) is ☀ = exp ( −V ) . Remark 2.1 . The following is an alternate way to introduce ...
Page 377
... bounded , uniformly continuous viscosity solution of the HJB equation ( 3.2 ) with the terminal data ( 3.3 ) . ( See comment following V ( 9.1 ) . ) By Lemma 4.1 , V * is a bounded uppersemicontinuous subsolution of ( 3.2 ) and by Lemma ...
... bounded , uniformly continuous viscosity solution of the HJB equation ( 3.2 ) with the terminal data ( 3.3 ) . ( See comment following V ( 9.1 ) . ) By Lemma 4.1 , V * is a bounded uppersemicontinuous subsolution of ( 3.2 ) and by Lemma ...
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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 brownian motion C₁ Cą(Q calculus of variations Chapter classical solution consider continuous on Q controlled Markov diffusion convergence convex Corollary D₂V defined definition denote deterministic dynamic programming equation dynamic programming principle Dynkin formula Example exists exit finite formula Hence HJB equation holds implies inequality initial data lateral boundary Lebesgue Lemma lim sup linear Lipschitz continuous Markov chain Markov control policy Markov processes maximum principle minimizing Moreover nonlinear obtain optimal control optimal Markov control partial derivatives partial differential equation proof of Theorem prove reference probability system Remark result satisfies second-order Section semiconvex stochastic control stochastic differential equation Suppose t₁ Theorem 5.1 uniformly continuous unique value function Verification Theorem viscosity solution viscosity subsolution viscosity supersolution yields