Generating random variates for stable sub-Gaussian processes with memory

We present a computationally efficient method to generate random variables from a univariate conditional probability density function (PDF) derived from a multivariate α-sub-Gaussian (αSG) distribution. The approach may be used to sequentially generate variates for sliding-window models that constrain immediately adjacent samples to be αSG random vectors. We initially derive and establish various properties of the conditional PDF and show it to be equivalent to a Student's t-distribution in an asymptotic sense. As the αSG PDF does not exist in closed form, we use these insights to develop a method based on the rejection sampling (accept-reject) algorithm that allows generating random variates with computational ease.