On the simulation of shot noise and some other random variables

Abstract

It is shown that the random voltage V t resulting from pulses with independent random amplitude Y i Poisson arrivals, and exponential decay, can be asymptotically represented, in the stationary case, by the following random variable; namely a sum of products of random variables: W= ∑ i=1 ∞ U iY i, where U i= ∏ j=1 i X j β/λ. Here X j are independent uniform random variables, β>0 is the decay parameter, λ>0 is the rate of the Poisson process.