  We present a new method to close the Master Equation representing the
continuous time dynamics of Ising interacting spins. The method makes use of
the the theory of Random Point Processes to derive a master equation for local
conditional probabilities. We analytically test our solution studying two known
cases, the dynamics of the mean field ferromagnet and the dynamics of the one
dimensional Ising system. We then present numerical results comparing our
predictions with Monte Carlo simulations in three different models on random
graphs with finite connectivity: the Ising ferromagnet, the Random Field Ising
model, and the Viana-Bray spin-glass model.
