The transition probability of a Cox-Ingersoll-Ross process can be represented by a non-central chi-square density. First we prove a new representation for the central chi-square density based on sums of powers of generalized Gaussian random variables. Second we prove Marsaglia's polar method...

The transition probability of a Cox–Ingersoll–Ross process can be represented by a non-central chi-square density. First, we establish a new representation for the central chi-square density based on sums of powers of generalized Gaussian random variables. Second, we show that Marsaglia's...