  We explore how the existence of a field with a heavy mass influences the low
energy dynamics of a quantum field with a light mass by expounding the
stochastic characters of their interactions which take on the form of
fluctuations in the number of (heavy field) particles created at the threshold,
and dissipation in the dynamics of the light fields, arising from the
backreaction of produced heavy particles. We claim that the stochastic nature
of effective field theories is intrinsic, in that dissipation and fluctuations
are present both above and below the threshold. Stochasticity builds up
exponentially quickly as the heavy threshold is approached from below, becoming
dominant once the threshold is crossed. But it also exists below the threshold
and is in principle detectable, albeit strongly suppressed at low energies. The
results derived here can be used to give a quantitative definition of the
`effectiveness' of a theory in terms of the relative weight of the
deterministic versus the stochastic behavior at different energy scales.
