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This paper addresses null controllability for both forward and backwardlinear stochastic parabolic equations by introducing convection terms on thedrift parts with bounded coefficients. Moreover, the forward stochasticparabolic equation includes a convection term on the diffusion part. The nullcontrollability results rely on novel Carleman estimates for both backward andforward stochastic parabolic equations, encompassing a divergence source terminterpreted in the weak sense. These Carleman estimates are established throughthe application of the duality technique. In doing so, we resolve somepreviously unanswered questions (see Remarks 2.1-2.2 in [S. Tang, and X. Zhang,SIAM J. Control Optim., 48 (2009), p.p 2191-2216]). Additionally, we present amore accurate estimation of the null-control costs.

Null Controllability for Stochastic Parabolic Equations with convection terms