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The long run behaviour of stochastic processes can be investigated by a variety of different methods. The random walk models and neural network models that we are interested in, have a structure that is eminently suitable for a probabilistic analysis based on the Law of Large Numbers (LLN) and its generalisations.

Here I will only discuss my recent research on stability properties of these models and the construction of their associated large time-space scaled limits. I will leave out the results on exponential stability properties [7] and probabilistic methods for this investigating this property, together with the research on asymptotic optimal control [4] and control of stochastic games, which both has been conducted at the Stieltjes institute during the past years.

Fri Mar 20 16:01:06 MET 1998