The Quadratic Variation of Gauss-Markov Semimartingales

Abstract

The covariance function of a Gauss-Markov process evaluated at points $(s,t)$ admits a representation as a product of a function of $\min (s,t)$ and a function of $\max (s,t)$. We call these functions the covariance factors of a Gauss-Markov process, and give the expression of the quadratic variation of a Gauss-Markov semimartingale in terms of its covariance factors.