Null controllability for backward stochastic parabolic convection-diffusion equations with dynamic boundary conditions

This paper deals with the null controllability for linear backward stochastic parabolic equations with dynamic boundary conditions and convection terms. Using the classical duality argument, the null controllability is achieved through an observability inequality of the corresponding adjoint equation. To establish this observability inequality, a new global Carleman estimate for forward stochastic parabolic equations in Sobolev spaces of negative order is developed. This Carleman estimate is derived by applying a duality technique. Additionally, we provide an estimate for the null-control cost.