Strong Error Estimates for a Space-Time Discretization of the Linear-Quadratic Control Problem with the Stochastic Heat Equation with Linear Noise

12/08/2020
by   Andreas Prohl, et al.
0

We propose a time-implicit, finite-element based space-time discretization of the necessary and sufficient optimality conditions for the stochastic linear-quadratic optimal control problem with the stochastic heat equation driven by linear noise of type [X(t)+σ(t)]dW(t), and prove optimal convergence w.r.t. both, space and time discretization parameters. In particular, we employ the stochastic Riccati equation as a proper analytical tool to handle the linear noise, and thus extend the applicability of the earlier work [16], where the error analysis was restricted to additive noise.

READ FULL TEXT

page 1

page 2

page 3

page 4

06/09/2020

A linear implicit Euler method for the finite element discretization of a controlled stochastic heat equation

We consider a numerical approximation of a linear quadratic control prob...
01/18/2019

Optimal Space-Time Block Code Designs Based on Irreducible Polynomials of Degree Two

The main of this paper is to prove that in terms of normalized density, ...
12/24/2020

A Space-Time DPG Method for the Heat Equation

This paper introduces an ultra-weak space-time DPG method for the heat e...
06/21/2022

The heat modulated infinite dimensional Heston model and its numerical approximation

The HEat modulated Infinite DImensional Heston (HEIDIH) model and its nu...
09/18/2020

A scalable algorithm for solving linear parabolic evolution equations

We present an algorithm for the solution of a simultaneous space-time di...
01/13/2021

Ergodicity of stochastic Cahn-Hilliard equations with logarithmic potentials driven by degenerate or nondegenerate noises

We study the asymptotic properties of the stochastic Cahn-Hilliard equat...