  Distributional fixed points of a Poisson shot noise transform (for
nonnegative, nonincreasing response functions bounded by 1) are characterized.
The tail behavior of fixed points is described. Typically they have either
exponential moments or their tails are proportional to a power function, with
exponent greater than -1. The uniqueness of fixed points is also discussed.
Finally, it is proved that in most cases fixed points are absolutely
continuous, apart from the possible atom at zero.
