On the simulation of shot noise and some other random variables

AbstractIt is shown that the random voltage Vt resulting from pulses with independent random amplitude Yi 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∞ UiYi, where Ui=∏j=1i Xjβ/λ. Here Xj are independent uniform random variables, β>0 is the decay parameter, λ>0 is the rate of the Poisson process