# Fractional Brownian Motion - Increments

There are a number of properties of Fractional Brownian Motion

Increments are (anti)correlated depending on the value of the Hurst parameter H, however, we also have that the increments are stationary according to this post:

distribution of fractional Brownian motion increments

What I don't understand is, a fBM path has a great deal of trend to it. So it has positively correlated increments. YET, the increments are symmetrically around zero (see link above). How is it possible for the increments to be symmetrically distributed around zero yet lead to a trend in the path. Thanks.

See here for the claim of increments being gaussian. Snip from textbook

I think you are confusing the increments $$dB_H(t)$$ with the process $$B_H(t)$$ itself.
The increments are stationary, the process itself is not. 'Centered' means the expected value of the increment is $$0$$. This does not mean that the increments are always $$0$$, and they can be positively or negatively correlated over time, corresponding to a positive or negative trend in the path.