Wiener Process

A Wiener process $W_t$ is a random process defined by:

• $W_0=0$ Almost surely
• $\forall s\le t$ we have that $W_t-W_s$ is independent of $W_s$.
• $\forall s\le t,W_s-W_t\sim \mathcal{N}(0,t-s)$, i.e. it is Normally distributed with Mean $0$ and Variance $t-s$.
• $W$ has Almost surely continuous paths.