  A Markov process fluctuating away from its typical behavior can be
represented in the long-time limit by another Markov process, called the
effective or driven process, having the same stationary states as the original
process conditioned on the fluctuation observed. We construct here this driven
process for diffusions spending an atypical fraction of their evolution in some
region of state space, corresponding mathematically to stochastic differential
equations conditioned on occupation measures. As an illustration, we consider
the Langevin equation conditioned on staying for a fraction of time in
different intervals of the real line, including the positive half-line which
leads to a generalization of the Brownian meander problem. Other applications
related to quasi-stationary distributions, metastable states, noisy chemical
reactions, queues, and random walks are discussed.
