Remarks on Some Applications

Summary

We now briefly sketch a few rather specific applied problems that suggest or even motivate a number of the questions taken up in this book. The aim will not be to give a full development, which would lie outside the scope and intent of the book, but rather to indicate how the problems arise and the mathematical questions suggested. References are given that will allow the intersted reader to look into the the details more extensively on his own. At times the description we give will be heuristic since there are still wide gaps in the mathematical development. This is especially so in an example from statistical mechanics. There is a brief discussion of a class of models in so-called “learning theory” in mathematical psychology. The last example is a resource flow model which is not probabilistic as usually given but obviously could be considered with a probabilistic interpretation. It is suggested formally by the Quesnay-Leontief models which have been of some interest in mathematical and statistical economics.