  We consider two reflecting diffusion processes $(X_t)_{t \ge 0}$ with a
moving reflection boundary given by a non-decreasing pure jump Markov process
$(R_t)_{t \ge 0}$. Between the jumps of the reflection boundary the diffusion
part behaves as a reflecting Brownian motion with negative drift or as a
reflecting Ornstein-Uhlenbeck process. In both cases at rate $\gamma(X_t -R_t)$
for some $\gamma \ge 0$ the reflection boundary jumps to a new value chosen
uniformly in $[R_{t-},X_t]$. Since after each jump of the reflection boundary
the diffusions are reflected at a higher level we call the processes Brownian
ratchet and Ornstein-Uhlenbeck ratchet. Such diffusion ratchets are
biologically motivated by passive protein transport across membranes. The
processes considered here are generalisations of the Brownian ratchet (without
drift) studied in (Depperschmidt and Pfaffelhuber, 2010). For both processes we
prove a law of large numbers, in particular each of the ratchets moves to
infinity at a positive speed which can be computed explicitly, and a central
limit theorem.
