Numerical analysis of a Neumann boundary control problem with a stochastic parabolic equation

被引：2

作者：

Zhou, Qin ^{[1
,2
]}

Li, Binjie ^{[1
]}

机构：

[1] Sichuan Univ, Sch Math, Chengdu 610064, Peoples R China

[2] China West Normal Univ, Sch Math, Nanchong 637002, Peoples R China

来源：

SCIENCE CHINA-MATHEMATICS | 2023年 / 66卷 / 09期

基金：

中国国家自然科学基金;

关键词：

Neumann boundary control; stochastic parabolic equation; Q-Wiener process; boundary noise; discretization; convergence; MAXIMUM PRINCIPLE; NOISE; DISCRETIZATION; APPROXIMATION; SIMULATION;

D O I：

10.1007/s11425-021-2027-7

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper analyzes the discretization of a Neumann boundary control problem with a stochastic parabolic equation, where an additive noise occurs in the Neumann boundary condition. The convergence is established for general filtration, and the convergence rate O(tau(1/4-epsilon)+h(1/2-epsilon)) is derived for the natural filtration of the Q-Wiener process.

引用

页码：2133 / 2156

页数：24

共 37 条

[1] A forward scheme for backward SDEs [J].

Bender, Christian ;

Denk, Robert .

STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2007, 117 (12) :1793-1812

[2] STOCHASTIC MAXIMUM PRINCIPLE FOR DISTRIBUTED PARAMETER-SYSTEMS [J].

BENSOUSSAN, A .

JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS, 1983, 315 (5-6) :387-406

[3] Discrete-time approximation and Monte-Carlo simulation of backward stochastic differential equations [J].

Bouchard, B ;

Touzi, N .

STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2004, 111 (02) :175-206

[4]

Brenner SC, 2008, The mathematical theory of finite element methods, V3rd, DOI DOI 10.1007/978-0-387-75934-0

[5] Error analysis of finite element approximations of the optimal control problem for stochastic Stokes equations with additive white noise [J].

Choi, Youngmi ;

Lee, Hyung-Chun .

APPLIED NUMERICAL MATHEMATICS, 2018, 133 :144-160

[6]

Da Prato G., 1993, Stoch. Int. J. Probab. Stoch. Process, V42, P167, DOI DOI 10.1080/17442509308833817

[7]

Da Prato G., 2014, Stochastic equations in infinite dimensions, DOI DOI 10.1017/CBO9781107295513

[8] Optimal control of a stochastic heat equation with boundary-noise and boundary-control [J].

Debussche, Arnaud ;

Fuhrman, Marco ;

Tessitore, Gianmario .

ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS, 2007, 13 (01) :178-205

[9] A MAXIMUM PRINCIPLE FOR OPTIMAL CONTROL OF STOCHASTIC EVOLUTION EQUATIONS [J].

Du, Kai ;

Meng, Qingxin .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2013, 51 (06) :4343-4362

[10] The forward-backward stochastic heat equation: Numerical analysis and simulation [J].

Dunst T. ;

Prohl A. .

SIAM Journal on Scientific Computing, 2016, 38 (05) :A2725-A2755

← 1 2 3 4 →