  In this paper, we establish two Carleman estimates for a stochastic
degenerate parabolic equation. The first one is for the backward stochastic
degenerate parabolic equation with singular weight function. Combining this
Carleman estimate and an approximate argument, we prove the null
controllability of the forward stochastic degenerate parabolic equation with
the gradient term. The second one is for the forward stochastic degenerate
parabolic equation with regular weighted function, based on which we obtain the
Lipschitz stability for an inverse problem of determining a random source
depending only on time in the forward stochastic degenerate parabolic equation.
