Exact controllability of stochastic parabolic equations with multiplicative noise

TL;DR

This paper proves that certain stochastic parabolic equations with multiplicative noise can be exactly controlled to reach zero state, advancing control theory for stochastic PDEs.

Contribution

It establishes the exact null controllability of linear and semilinear stochastic parabolic equations with finite modes of multiplicative noise, a novel result in stochastic control.

Findings

Linear stochastic parabolic equations are exactly null controllable.

Semilinear stochastic parabolic equations are also exactly null controllable.

Controllability holds with a finite number of noise modes.

Abstract

One proves that the linear and semilinear stochastic parabolic equations with a multiplicative noise with a finite number of modes are exactly null controllable.