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. |
From inside the book
Results 1-3 of 50
Page 193
... Similarly , ( 8.14b ) follows from ( 8.10 ) . IV.9 Estimates for second - order difference quotients = We will now obtain a bound for second difference quotients A2J △ J ( t , · , u ) . This will imply a one - sided bound ( 9.7 ) for ...
... Similarly , ( 8.14b ) follows from ( 8.10 ) . IV.9 Estimates for second - order difference quotients = We will now obtain a bound for second difference quotients A2J △ J ( t , · , u ) . This will imply a one - sided bound ( 9.7 ) for ...
Page 198
... Similarly , the generalized partial derivatives Vt , Vr 、 z , ( if they exist ) are defined as those functions in Loc ( Qo ) such that , for all • € Co ( Qo ) , Vi ( 10.2 ) ( 10.3 ) V1dxdt = - Vo + dxdt , Qo Qo √ Vz1z , & dødt = So ...
... Similarly , the generalized partial derivatives Vt , Vr 、 z , ( if they exist ) are defined as those functions in Loc ( Qo ) such that , for all • € Co ( Qo ) , Vi ( 10.2 ) ( 10.3 ) V1dxdt = - Vo + dxdt , Qo Qo √ Vz1z , & dødt = So ...
Page 377
... Similarly , V. is a viscosity supersolu- tion . We assume that ( 3.1 ) and IV ( 2.2 ) hold . Let V ( t , x ) be the value function for the controlled diffusion process , as in IV ( 2.10 ) . We also make the following assumption , which ...
... Similarly , V. is a viscosity supersolu- tion . We assume that ( 3.1 ) and IV ( 2.2 ) hold . Let V ( t , x ) be the value function for the controlled diffusion process , as in IV ( 2.10 ) . We also make the following assumption , which ...
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