# Sigma-martingale

An $\mathbb{R}^d$-valued stochastic process $X = (X_t)_{t = 0}^T$ is a sigma-martingale if it is a semimartingale and there exists an $\mathbb{R}^d$-valued martingale M and an M-integrable predictable process $\phi$ with values in $\mathbb{R}_+$ such that
$X = \phi \cdot M. \,$[1]