  We study a directed stochastic sandpile model of Self-Organized Criticality,
which exhibits recurrent, multiple topplings, putting it in a separate
universality class from the exactly solved model of Dhar and Ramaswamy. We show
that in the steady-state all stable states are equally likely. Then we
explicitly derive a discrete dynamical equation for avalanches on the lattice.
By coarse-graining we arrive at a continuous Langevin equation for the
propagation of avalanches and calculate all the critical exponents
characterizing them. The avalanche equation is similar to the Edwards-Wilkinson
equation, but with a noise amplitude that is a threshold function of the local
avalanche activity, or interface height, leading to a stable absorbing state
when the avalanche dies. It represents a new type of absorbing state phase
transition.
