  In this note, we present a version of Hoeffding's inequality in a
continuous-time setting, where the data stream comes from a uniformly ergodic
diffusion process. Similar to the well-studied case of Hoeffding's inequality
for discrete-time uniformly ergodic Markov chain, the proof relies on
techniques ranging from martingale theory to classical Hoeffding's lemma as
well as the notion of deviation kernel of diffusion process. We present two
examples to illustrate our results. In the first example we consider large
deviation probability on the occupation time of the Jacobi diffusion, a popular
process used in modelling of exchange rates in mathematical finance, while in
the second example we look at the exponential functional of a finite interval
analogue of the Ornstein-Uhlenbeck process introduced by Kessler and
S{\o}rensen (1999).
