  We investigate the low-temperature dynamics of a simple stochastic model,
introduced recently in the context of the physics of glasses. The slowest
characteristic time at equilibrium diverges exponentially at low temperature.
On smaller time scales, the nonequilibrium dynamics of the system exhibits an
aging regime. We present an analytical study of the scaling behaviour of the
mean energy, of its local correlation and response functions, and of the
associated fluctuation-dissipation ratio throughout the regime of low
temperature and long times. This analysis includes the aging regime, the
convergence to equilibrium, and the crossover behaviour between them.
