A second-order maximum principle for singular optimal stochastic controls
Shanjian Tang
Discrete & Continuous Dynamical Systems - B 2010, 14(4): 1581-1599 doi: 10.3934/dcdsb.2010.14.1581
A singular optimal stochastic control problem is studied. A second-order maximum principle is presented. The second-order adjoint processes are involved, though the diffusion of the control system is control independent. The range theorem of vector-valued measures is used to prove the maximum principle. Examples are given to illustrate the applications.
keywords: first and second adjoint processes vector-valued measure theory. second-order maximum principle Singular optimal stochastic control spike variation
Nonlinear backward stochastic evolutionary equations driven by a space-time white noise
Ying Hu Shanjian Tang
Mathematical Control & Related Fields 2018, 8(3&4): 739-751 doi: 10.3934/mcrf.2018032

We study the well solvability of nonlinear backward stochastic evolutionary equations driven by a space-time white noise. We first establish a novel a priori estimate for solution of linear backward stochastic evolutionary equations, and then give an existence and uniqueness result for nonlinear backward stochastic evolutionary equations. A dual argument plays a crucial role in the proof of these results. Finally, an example is given to illustrate the existence and uniqueness result.

keywords: Backward stochastic evolutionary equation space-time white noise well solvability a priori estimate dual argument

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