  The following random recurrency: $$ W_{n+1} = U_{n+1} ( W_n + \Lambda_{n+1} )
$$ where $W_{-1}=0.$ is known to be associated with the shot noise : $$ W_{t} =
\sum_{0<t_k<t} \Lambda_{k} e^{-(t-t_k)} $$ where the $t_k$ are the dates of a
Poisson process, the $ U_i ;\ i = 0,1,... $ are independent uniform variables.
This can be extended to the triggered shot noise : $$ W_{t} = \sum_{0<t_{lk}<t}
\Lambda_{lk} e^{-(t-t_{lk})} , l=1,2,3,... $$ The random amplitudes
$\Lambda_i,\ i = 0,1,... $ are positive Dufresne independent variables or also
even density variables which characteristic function given by generalized
hypergeometric function.
  Keywords: Random Difference Equations,Triggered Shot Noise, Iterated
Cosine-Bessel functions, Logarithmic Distribution Functions,Saddle Point
Method, Asymptotic Calculations, Generalized Hypergeometric Functions, Psi
Functions.
