The fundamental notions in connection with Markov chains
Ehrhard Behrends · Advanced lectures in mathematics · 2000
What is essential? It is one thing to fix a set of axioms as the starting point of a hopefully interesting new theory. However, it is usually much more difficult to find the relevant notions which enable one to study — sometimes even to completely classify — the new objects. Examples are very rare where this has been achieved by a single mathematician. Generally it takes years or decades where many suggestions are under consideration, where it turns out to be necessary to modify the axioms and where many researchers are involved.