I'm trying to prove whether a given process is a submartingale.
Let $W = \{W_t, t ≥ 0\}$ - m-dimensional Brownian motion.
Prove that $( ||W_t||, F_t )_{t ≥ 0}$ is a submartingale (with a.s. continuous trajectories), where $||\cdot||$ is the Euclidean norm in R^m.