Inverse problems for stochastic parabolic equations with additive noise

In this paper, we study two inverse problems for stochastic parabolic equations with additive noise. One is to determinate the history of a stochastic heat process and the random heat source simultaneously by the observation at the final time T. For this inverse problem, we obtain a conditional stability result. The other one is an inverse source problem to determine two kinds of sources simultaneously by the observation at the final time and on the lateral boundary. The main tool for solving the inverse problems is a new global Carleman estimate for the stochastic parabolic equation.

Automated summary

This paper investigates two inverse problems for stochastic parabolic equations, one involving determining the history of a stochastic heat process and the random heat source, and the other involving determining two kinds of sources simultaneously. A new global Carleman estimate for the stochastic parabolic equation is the main tool for solving these inverse problems, leading to a conditional stability result.