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.
Categories: math.PR