  We show that gamma distributions, generalized positive Linnik distributions,
S2 distributions are fixed points of Poisson shot noise transforms. The
corresponding response functions are identified via their inverse functions
except for some special cases when those can be obtained explicitly. As a
by-product, it is proven that log-convexity of the response function is not
necessary for selfdecomposability of non-negative Poisson shot noise
distribution. Some attention is given to perpetuities of a rather special type
which are closely related to our model. In particular, we study the problem of
their existence and uniqueness.
