We define a semi-min-stable (SMS) process
Y(t) in
to be one which is stable under the simultaneous operations of taking the minima of
n independent copies of
Y(t) (pointwise over time
t) and rescaling space and time. We show that the only possible rescaling of time is by a fixed power of
n and that SMS processes are essentially the only possible weak limits for large
... [Show full abstract] m of a process obtained by taking the minimum, pointwise over t, of m independent copies of a given process and then rescaling space and time. We describe the representation of a SMS process as the minimum of a Poisson process on a function space. We obtain a partial characterization of sample continuous SMS processes, similar to that of de Haan in the case of max-stable processes.