  The main result is a counterpart of the theorem of Monroe [\emph{Ann.
Probability} \textbf{6} (1978) 42--56] for a geometric Brownian motion: A
process is equivalent to a time change of a geometric Brownian motion if and
only if it is a nonnegative supermartingale. We also provide a link between our
main result and Monroe [\emph{Ann. Math. Statist.} \textbf{43} (1972)
1293--1311]. This is based on the concept of a \emph{minimal} stopping time,
which is characterised in Monroe [\emph{Ann. Math. Statist.} \textbf{43} (1972)
1293--1311] and Cox and Hobson [\emph{Probab. Theory Related Fields}
\textbf{135} (2006) 395--414] in the Brownian case. We finally suggest a
sufficient condition for minimality (for the processes other than a Brownian
motion) complementing the discussion in the aforementioned papers.
