High density shot noise and gaussianity

The distance from Gaussianity of the shot noise process is considered, where t i are the random times of a Poisson process with average density λ ( t ) . With F ( x ) the distribution function of x ( t ) and G ( x ) that of a normal process with the same mean and variance as x ( t ) it is shown that where If the process x ( t ) is stationary with λ( t ) = λ and h ( t , τ) = h ( t – τ ) and the function h ( t ) is bandlimited by ω c , then the above yields