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 41
... term on the right side of ( 9.7 ) tends to L ( s , xp ( s ) , v ) – L ( 8 , XR ( 8 ) , UR ( 8 ) ) . By the mean value theorem , the second term equals [ “ fa 8 + 8 Lx ( r , xp ( r ) + 8XÇε , up ( r ) ) · Sådλdr , which tends as 8 → 0 ...
... term on the right side of ( 9.7 ) tends to L ( s , xp ( s ) , v ) – L ( 8 , XR ( 8 ) , UR ( 8 ) ) . By the mean value theorem , the second term equals [ “ fa 8 + 8 Lx ( r , xp ( r ) + 8XÇε , up ( r ) ) · Sådλdr , which tends as 8 → 0 ...
Page 132
... term on the right side of ( 4.6 ) comes from the deterministic evolution of x ( s ) during intervals of constancy of z ( s ) , as in Example ( b ) , and the last term comes from the parameter process z ( s ) . Example ( c ) is a special ...
... term on the right side of ( 4.6 ) comes from the deterministic evolution of x ( s ) during intervals of constancy of z ( s ) , as in Example ( b ) , and the last term comes from the parameter process z ( s ) . Example ( c ) is a special ...
Page 177
... term ( 1 - u1 ( s ) ) x ( s ) in ( 5.18 ) is negative . This term represents money borrowed by the investor ; and it has been implicitly as- sumed that money is borrowed at the same rate a as the return rate for the riskless asset ...
... term ( 1 - u1 ( s ) ) x ( s ) in ( 5.18 ) is negative . This term represents money borrowed by the investor ; and it has been implicitly as- sumed that money is borrowed at the same rate a as the return rate for the riskless asset ...
Contents
Viscosity Solutions | 53 |
Controlled Markov Diffusions in R | 157 |
SecondOrder Case | 213 |
Copyright | |
7 other sections not shown
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