  The generalized grey Brownian motion is a time continuous self-similar with
stationary increments stochastic process whose one dimensional distributions
are the fundamental solutions of a stretched time fractional differential
equation. Moreover, the distribution of the time-changed Brownian motion by an
inverse stable process solves the same equation, hence both processes have the
same one dimensional distribution. In this paper we show the mutual singularity
of the probability measures on the path space which are induced by generalized
grey Brownian motion and the time-changed Brownian motion though they have the
same one dimensional distribution. This singularity property propagates to the
probability measures of the processes which are solutions to the stochastic
differential equations driven by these processes.

Probability