  The question how the extremal values of a stochastic process achieved on
different time intervals are correlated to each other has been discussed within
the last few years on examples of the running maximum of a Brownian motion, of
a Brownian Bridge and of a Slepian process. Here, we focus on the two-time
correlations of the running range of Brownian motion - the maximal extent of a
Brownian trajectory on a finite time interval. We calculate exactly the
covariance function of the running range and analyse its asymptotic behaviour.
Our analysis reveals non-trivial correlations between the value of the largest
descent (rise) of a BM from the top to a bottom on some time interval, and the
value of this property on a larger time interval.
