Abstract. 
The statistical properties of dynamical systems are traditionally studied
in the context of their invariant measures. Motivated by non-equilibrium 
phenomena in nature, we wish to step out of the above setup. To this end,
we introduce a model whose characteristics change slowly with time. Solving 
a martingale problem in the spirit of Stroock and Varadhan, we show that 
repeated observations of the state of the system yield a certain stochastic 
diffusion process.