Brownian increment
= Brownian increment
{c}
{title2=$W_t-W_s$}
An increment of a <Brownian motion> between deterministic times $s<t$ is $W_t-W_s$. It has <normal distribution> $N(0,t-s)$ and is independent of the filtration up to time $s$. Increments on disjoint time intervals are independent. Their <covariance> is the length of overlap of the corresponding intervals; this also follows from the <Brownian covariance kernel>.