Diffusion Processes with Hidden States from ... - FU Berlin, FB MI

1 Motivation„NEC FASCES, NEC OPES,SOLA ARTIS SCEPTRA PERENNANT“ [57, p. 105]”Neither high agencies, nor power,solely the scepter of science outlast”(Tycho Brahe, motto, carved in stone over the north entranceof the Stjerneborg observatory, built by Brahe in the year 1584) 1Within living memory or at least since humanity has emerged conscious awareness, we possessa quenchless desire to give sense to all what we percept. At all times mankind has the wish tounderstand its surrounding environment, and this wish is inseparably correlated with the fact thatwe inevitably create models when we adept a certain phenomenon in nature.A model is in general an image of the phenomenon, an image that we make, in order to understandand maybe forecast future phenomena. Models are emerging in our brains backwards, meaningthat experience is coming first and afterwards is leading to a model. Though other, earlier thoughtmodels can be the basis of our new models it is at least experience that enables us to estimate anew model.A model in mathematical sense is a set of mathematical objects that are connected with each otherby functional relationships.A Theory is an aggregation of different models and they are described by a set of axioms that buildup the basis of the theory. Propositions can be derived from these axioms within the theory, andpropositions in turn can be checked by observation. While the propositions can be tracked backto the axioms of a theory, there is no proof in a mathematical sense for the axioms themselves,axioms are moreover convention.As such, theories can not be proved at last but in the best case experience a kind of endorsement.Endorsement by numerous observations is verifying different propositions of the theory. Neverthelessa theory is never immune against falsification of at least one of it’s propositions. Thus atheory can be falsified but not verified in perpetuity.A good theory is characterized by its capability to combine and interconnect such phenomena thaton first sight have not much to do with each other. By this a theory has a more universality than a1 German translation: „Weder hohe Ämter, noch Macht, einzig die Zepter der Wissenschaft überdauern“ - TychoBrahe.1