Noise and Full Counting Statistics of Incoherent Multiple Andreev Reflection

We present a general theory for the full counting statistics of multiple Andreev reflections in incoherent superconducting-normal-superconducting contacts. The theory, based on a stochastic path integral approach, is applied to a superconductor-double-barrier system. It is found that all cumulants of the current show a pronounced subharmonic gap structure at voltages V=2Delta/en. For low voltages V<<Delta/e, the counting statistics results from diffusion of multiple charges in energy space, giving the pth cumulant Q(p) proportional, variantV(2-p), diverging for p> or =3. We show that this low-voltage result holds for a large class of incoherent superconducting-normal-superconducting contacts.