  Sample Space Reducing (SSR) processes are simple stochastic processes that
offer a new route to understand scaling in path-dependent processes. Here we
define a cascading process that generalises the recently defined SSR processes
and is able to produce power laws with arbitrary exponents. We demonstrate
analytically that the frequency distributions of states are power laws with
exponents that coincide with the multiplication parameter of the cascading
process. In addition, we show that imposing energy conservation in SSR cascades
allows us to recover Fermi's classic result on the energy spectrum of cosmic
rays, with the universal exponent -2, which is independent of the
multiplication parameter of the cascade. Applications of the proposed process
include fragmentation processes or directed cascading diffusion on networks,
such as rumour or epidemic spreading.
