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 4
... Example 2.3 . If U = [ -a , a ] with a < ∞ , it is an example of a linear regulator problem with a saturation constraint . One can also consider the problem of controlling the solution x ( s ) = ( x1 ( s ) , x2 ( s ) ) to ( 2.4 ) on an ...
... Example 2.3 . If U = [ -a , a ] with a < ∞ , it is an example of a linear regulator problem with a saturation constraint . One can also consider the problem of controlling the solution x ( s ) = ( x1 ( s ) , x2 ( s ) ) to ( 2.4 ) on an ...
Page 29
... example , in which O is the interval ( 0 , ∞ ) . Example 7.3 . This example and Example 7.4 concern the consumption and investment behavior of a single agent . In the simplest version of the model , the agent has wealth x ( s ) ...
... example , in which O is the interval ( 0 , ∞ ) . Example 7.3 . This example and Example 7.4 concern the consumption and investment behavior of a single agent . In the simplest version of the model , the agent has wealth x ( s ) ...
Page 31
Wendell Helms Fleming, H. Mete Soner. Example 7.4 . Continuing Example 7.3 , let us now suppose that the agent has access to two assets . Each asset has a fixed rate of return , with respective interest rates a and A ( 0 < a < A ) . At ...
Wendell Helms Fleming, H. Mete Soner. Example 7.4 . Continuing Example 7.3 , let us now suppose that the agent has access to two assets . Each asset has a fixed rate of return , with respective interest rates a and A ( 0 < a < A ) . At ...
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 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