[radikalus]

This is slick...but:

How often do you want to generate random walks of this type where the variance of the process isn't dependent on its current level?

Observe that, as you increase the standard deviation of the random normal (to even .1), your "random walk" always walks to zero.

I don't mean to be a beady-eyed-pterodactyl but, as cool as clever one-liners sometimes are, often they solve toy problems. I say this as someone who loves R and uses it everyday and constantly is forced to brute-force with ugly inlined Rcpp code. (Which is fine)

[mariuskempe]

That's an interesting point. In fact, the expectation of the random walk is always the same as its starting value, because, although most of the walks go to 0 like you observed, there are very occasionally walks that drift upward to astronomical values.

As for the usefulness of this kind of walk: the process we're modelling is an evolutionary one, where the rate of change is fixed (in this case within the species) and we'd like to detect 'random' (non-selected) evolutionary paths by comparing simulations to historical data.