We introduce a stochastic partial differential equation capable
of reproducing the main features of spatiotemporal
intermittency (STI). Additionally the model displays a noise
induced transition from laminarity to the STI regime. We show by
numerical simulations and a mean-field analysis that for high
noise intensities the system globally evolves to a uniform
absorbing phase, while for noise intensities below a critical
value spatiotemporal intermittence dominates. A quantitative
computation of the loci of this transition in the relevant
parameter space is presented.