A functional analytic approach to infinite dimensional stochastic linear systems

2020/05/14 by Fatima-Zahra Lahbiri, Lahbiri, Fatima-Zahra, Saïd Hadd +2
Economics, Econometrics and Finance · Engineering · Mathematics · #93B35 #93C05 #93C73 #93E03 #FOS: Mathematics #Nonlinear Differential Equations Analysis #Optimization and Control (math.OC) #Stability and Controllability of Differential Equations #Stochastic processes and financial applications #math.OC #msc:93B35 #msc:93C05 #msc:93C73 #msc:93E03

paper · pdf · doi:10.48550/arxiv.2005.07254

openalex publication_date 2020/05/14 · arxiv created 2021/05/27 · arxiv updated 2021/05/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we study infinite dimensional stochastic systems having both unbounded control and observation operators. First of all, using a semigroup approach, we give another take of the well-posedness of such systems treated in [SIAM J. Control Optim., 53 (2015), pp. 3457--3482]. We further prove a result on the exact controllability of such systems. Second, we propose a new variation of constants formula for mild solutions of perturbed abstract stochastic Cauchy problems using the concept of Yosida extensions of admissible operators. Third, we prove the well-posedness of perturbed boundary control systems. Fourth, we apply this result to a general class of stochastic systems with delays in the state, control, and observation parts. Finally, we study admissible observation operators and exact observability for semilinear stochastic systems.

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