  By a general shot noise process we mean a shot noise process in which the
counting process of shots is arbitrary locally finite. Assuming that the
counting process of shots satisfies a functional limit theorem in the Skorokhod
space with a locally H\"{o}lder continuous Gaussian limit process and that the
response function is regularly varying at infinity we prove that the
corresponding general shot noise process satisfies a similar functional limit
theorem with a different limit process and different normalization and
centering functions. For instance, if the limit process for the counting
process of shots is a Brownian motion, then the limit process for the general
shot noise process is a Riemann-Liouville process. We specialize our result for
five particular counting processes. Also, we investigate H\"{o}lder continuity
of the limit processes for general shot noise processes.
