Flow Control as a Stochastic Optimal Control Problem with Incomplete Information
Problems of Information Transmission
Stochastic PDIEs and backward doubly stochastic differential equations driven by Lévy processes
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
Journal of Computational and Applied Mathematics
Optimal control of a stochastic system: state-costate analysis
MIC '07 Proceedings of the 26th IASTED International Conference on Modelling, Identification, and Control
On solutions to backward stochastic partial differential equations for Lévy processes
Journal of Computational and Applied Mathematics
SIAM Journal on Control and Optimization
Infinite horizon optimal control of forward-backward stochastic differential equations with delay
Journal of Computational and Applied Mathematics
Stochastic Near-Optimal Singular Controls for Jump Diffusions: Necessary and Sufficient Conditions
Journal of Dynamical and Control Systems
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A maximum principle is proved for optimal controls of stochastic systems with random jumps. The control is allowed to enter into both diffusion and jump terms. The form of the maximum principle turns out to be quite different from the one corresponding to the pure diffusion system (the word "pure" here means the absence of the jump term). In calculating the first-order coefficient for the cost variation, only a property for Lebesgue integrals of scalar-valued functions in the real number space ${\Cal R}$ is used. This shows that there is no essential difference between deterministic and stochastic systems as far as the derivation of maximum principles is concerned.