This paper is addressed to proving a new Carleman estimate for stochastic parabolicequations. Compared to the existing Carleman estimate in this respect (see [S. Tang and X.Zhang, SIAM J. Control Optim. 48 (2009) 2191–2216.], Thm.5.2), one extra gradient term involving in that estimate is eliminated. Also, our improvedCarleman estimate is established by virtue of the known Carleman estimate fordeterministic parabolic equations. As its application, we prove the existence ofinsensitizing controls for backward stochastic parabolic equations. As usual, thisinsensitizing control problem can be reduced to a partial controllability problem for asuitable cascade system governed by a backward and a forward stochastic parabolicequation. In order to solve the latter controllability problem, we need to use ourimproved Carleman estimate to establish a suitable observability inequality for somelinear cascade stochastic parabolic system, while the known Carleman estimate for forwardstochastic parabolic equations seems not enough to derive the desired inequality.
