3,216 research outputs found
Maximum Principle for Forward-Backward Doubly Stochastic Control Systems and Applications
The maximum principle for optimal control problems of fully coupled
forward-backward doubly stochastic differential equations (FBDSDEs in short) in
the global form is obtained, under the assumptions that the diffusion
coefficients do not contain the control variable, but the control domain need
not to be convex. We apply our stochastic maximum principle (SMP in short) to
investigate the optimal control problems of a class of stochastic partial
differential equations (SPDEs in short). And as an example of the SMP, we solve
a kind of forward-backward doubly stochastic linear quadratic optimal control
problems as well. In the last section, we use the solution of FBDSDEs to get
the explicit form of the optimal control for linear quadratic stochastic
optimal control problem and open-loop Nash equilibrium point for nonzero sum
differential games problem
A maximum principle for controlled time-symmetric forward-backward doubly stochastic differential equation with initial-terminal sate constraints
In this paper, we study the optimal control problem of a controlled
time-symmetric forward-backward doubly stochastic differential equation with
initial-terminal sate constraints. Applying the terminal perturbation method
and Ekeland's variation principle, a necessary condition of the stochastic
optimal control, i.e., stochastic maximum principle is derived. Applications to
backward doubly stochastic linear-quadratic control models are investigated.Comment: 22 page
On Backward Doubly Stochastic Differential Evolutionary System
In this paper, we are concerned with backward doubly stochastic differential
evolutionary systems (BDSDESs for short). By using a variational approach based
on the monotone operator theory, we prove the existence and uniqueness of the
solutions for BDSDESs. We also establish an It\^o formula for the Banach
space-valued BDSDESs.Comment: 33 page
The Equivalence between Uniqueness and Continuous Dependence of Solution for BDSDEs
In this paper, we prove that, if the coefficient f = f(t; y; z) of backward
doubly stochastic differential equations (BDSDEs for short) is assumed to be
continuous and linear growth in (y; z); then the uniqueness of solution and
continuous dependence with respect to the coefficients f, g and the terminal
value are equivalent.Comment: 11 page
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