  We give the description of the following model:
  $$ U_{n}=X_{n}(Y_{n}+U_{n-1})$$ for $n>1$ in the case where the $X_{n}$ are
i.d.d. random variables with probability density: $$ A x^{A-1} , x \in [0,1]
,$$
  $A$ is also a random variable distributed according to a Gamma law.
  The $ Y_{n}$ are or deterministic and equal to $1$ or independent Gamma
random variables.
  We use this model to compute the shot noise with random parameters.
  Keywords: Random difference equations, Shot noise, Volterra functions,
differential-difference equations, Monte-carlo simulation.
