Markovian chi-square and gamma processes

A sequence {Xn, n [greater-or-equal, slanted] 1} of random variables such that each Xn has chi-square or gamma distribution can be generated from independent Gaussian sequences. We study the properties of such sequences. The Markov property of gamma and chi-square sequences is characterized. The extension of these results to continuous time processes is indicated. A general gamma Markov model based on sums of random numbers of independent exponential and gamma random variables is formulated and its properties are investigated.