The changes in any non-overlapping time increments are independent.
Formally:
\(t_0<t_1<t_2<...<t_m\)
With \(X_t\)
\(X_{t_1}-X_{t_0}\) is indepentent from \(X_{t_2}-X{t_1}\) etc.
A Wiener process is a process \(W_t\) with independent increments, which: + Is continuous + Has normally distributed increments.
Can be constructed as limit of random walk. Can also be constructed as integral of Gaussian noise?
brownian motion in stats. given we start at a, what is chance be end up at b? normal. do 1d then multi d