  We introduce and test an algorithm that adaptively estimates large deviation
functions characterizing the fluctuations of additive functionals of Markov
processes in the long-time limit. These functions play an important role for
predicting the probability and pathways of rare events in stochastic processes,
as well as for understanding the physics of nonequilibrium systems driven in
steady states by external forces and reservoirs. The algorithm uses methods
from risk-sensitive and feedback control to estimate from a single trajectory a
new process, called the driven process, known to be efficient for importance
sampling. Its advantages compared to other simulation techniques, such as
splitting or cloning, are discussed and illustrated with simple equilibrium and
nonequilibrium diffusion models.

Statistical Mechanics