2024/12/24 by Qiming Wang, Wang, Qiming, Wanfang Shen +3
Economics, Econometrics and Finance · Engineering · Environmental Science · #49J20 #65M60 #93E20 #Advanced Numerical Methods in Computational Mathematics #Analysis of environmental and stochastic processes #FOS: Mathematics #Optimization and Control (math.OC) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2412.18173
openalex publication_date 2024/12/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, the optimal strong error estimates for stochastic parabolic optimal control problem with additive noise and integral state constraint are derived based on time-implicit and finite element discretization. The continuous and discrete first-order optimality conditions are deduced by constructing the Lagrange functional, which contains forward-backward stochastic parabolic equations and a variational equation. The fully discrete version of forward-backward stochastic parabolic equations is introduced as an auxiliary problem and the optimal strong convergence orders are estimated, which further allows the optimal a priori error estimates for control, state, adjoint state and multiplier to be derived. Then, a simple and yet efficient gradient projection algorithm is proposed to solve stochastic parabolic control problem and its convergence rate is proved. Numerical experiments are carried out to illustrate the theoretical findings.