6,733 research outputs found
Stochastic Minimum Principle for Partially Observed Systems Subject to Continuous and Jump Diffusion Processes and Driven by Relaxed Controls
In this paper we consider non convex control problems of stochastic
differential equations driven by relaxed controls. We present existence of
optimal controls and then develop necessary conditions of optimality. We cover
both continuous diffusion and Jump processes.Comment: Pages 23, Submitted to SIAM Journal on Control and Optimizatio
Optimal distributed control of a stochastic Cahn-Hilliard equation
We study an optimal distributed control problem associated to a stochastic
Cahn-Hilliard equation with a classical double-well potential and Wiener
multiplicative noise, where the control is represented by a source-term in the
definition of the chemical potential. By means of probabilistic and analytical
compactness arguments, existence of an optimal control is proved. Then the
linearized system and the corresponding backward adjoint system are analysed
through monotonicity and compactness arguments, and first-order necessary
conditions for optimality are proved.Comment: Key words and phrases: stochastic Cahn-Hilliard equation, phase
separation, optimal control, linearized state system, adjoint state system,
first-order optimality condition
Controlled diffusion processes
This article gives an overview of the developments in controlled diffusion
processes, emphasizing key results regarding existence of optimal controls and
their characterization via dynamic programming for a variety of cost criteria
and structural assumptions. Stochastic maximum principle and control under
partial observations (equivalently, control of nonlinear filters) are also
discussed. Several other related topics are briefly sketched.Comment: Published at http://dx.doi.org/10.1214/154957805100000131 in the
Probability Surveys (http://www.i-journals.org/ps/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Subjective Equilibria under Beliefs of Exogenous Uncertainty
We present a subjective equilibrium notion (called "subjective equilibrium
under beliefs of exogenous uncertainty (SEBEU)" for stochastic dynamic games in
which each player chooses its decisions under the (incorrect) belief that a
stochastic environment process driving the system is exogenous whereas in
actuality this process is a solution of closed-loop dynamics affected by each
individual player. Players observe past realizations of the environment
variables and their local information. At equilibrium, if players are given the
full distribution of the stochastic environment process as if it were an
exogenous process, they would have no incentive to unilaterally deviate from
their strategies. This notion thus generalizes what is known as the
price-taking equilibrium in prior literature to a stochastic and dynamic setup.
We establish existence of SEBEU, study various properties and present explicit
solutions. We obtain the -Nash equilibrium property of SEBEU when
there are many players
- …