The Wiener process is defined by the three properties:
1. W(0)$W(0) = 00$,
2. W(t)$W(t)$ is almost surely continuous, and
3. W(t)$W(t)$ has independent increments with W(t)$W(t) - W(s) ~\sim N(0, t-s)t-s)$ (for $0 ≤ s < t)t$).
What would be an example of a process which satisfies 1) and 3), but not 2) ?
I am going to teach an introductory class on Brownian motion at advanced undergrad level.
Just wanted to make sure that all the conditions are mutually independent.