The Quadratic Variation of Gauss-Markov Semimartingales

TL;DR

This paper characterizes the quadratic variation of Gauss-Markov semimartingales using their covariance factors, providing a new analytical framework for understanding their stochastic properties.

Contribution

It introduces the concept of covariance factors for Gauss-Markov processes and derives an explicit expression for the quadratic variation in terms of these factors.

Findings

Quadratic variation expressed via covariance factors.

Representation of covariance function as a product of functions.

Analytical framework for 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.