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 157
... stochastic differential equation of the form ( 2.1 ) . Section 2 is concerned with the formulation of finite time horizon control problems for Markov diffusions , where control occurs until exit from a given cylindrical region QC R + 1 ...
... stochastic differential equation of the form ( 2.1 ) . Section 2 is concerned with the formulation of finite time horizon control problems for Markov diffusions , where control occurs until exit from a given cylindrical region QC R + 1 ...
Page 254
... stochastic differential equation ( 2.1 ) dx = b ( s , x ( s ) ) ds + o ( s , x ( s ) ) dw ° ( s ) , with initial data x ( t ) = x . In ( 2.1 ) , σ ( s , x ) is an n x n nonsingular matrix and w ( ) is an F , -adapted brownian motion on ...
... stochastic differential equation ( 2.1 ) dx = b ( s , x ( s ) ) ds + o ( s , x ( s ) ) dw ° ( s ) , with initial data x ( t ) = x . In ( 2.1 ) , σ ( s , x ) is an n x n nonsingular matrix and w ( ) is an F , -adapted brownian motion on ...
Page 397
Wendell Helms Fleming, H. Mete Soner. Appendix D Stochastic Differential Equations : Random Coefficients In this appendix we review some results about Ito - sense stochastic differ- ential equations , with random ( progressively ...
Wendell Helms Fleming, H. Mete Soner. Appendix D Stochastic Differential Equations : Random Coefficients In this appendix we review some results about Ito - sense stochastic differ- ential equations , with random ( progressively ...
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 Cą(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