I've just started to study random processes and I'm trying to solve the following problem:
Let $W(t)$ be a Brownian motion with filtration $F(t)$ generated by $ W(t)$ (i.e., $F(t)=\sigma \left( W(s)\right) $, $s \in [0,t]$).
- Is the process $|W(t)|$ a sub martingale? A super martingale? Or neither?
- Is $|W(t)|$ a Markov process?
Unfortunately, I can't see how to do that using the definition of sub/super martingale.. Any help will be appreciated!