A quantitative law of large numbers via exponential martingales

We propose a direct, quantitative technique for studying the asymptotic distribution of sequences of Markov processes in infinite dimensions. The "fluid limit" of such a sequence is constructed from the limiting generator, and convergence relies on the properties of an associated sequence of exponential martingales. Through a suitable localisation of the processes we obtain tight bounds on the deviation probabilities uniformly in all co-ordinates. Hence we are able to overcome the difficulties arising from an infinite-dimensional state space.