In this paper we explore the mathematical and epistemological connections between the stochastic derivation of the Schr\"odinger equation and the one proposed by ourselves in previous papers. It will be shown that these connections are accomplished by means of the fluctuation-dissipation theorem, to which we may unambiguously relate the symbols and physical references of both approaches. As a by-product of our investigation, it will be possible to interpret the time-energy dispersion relation on sounder grounds. It will also be possible to discuss the superposition principle and to interpret it on a quite simple basis. The origin of the stochasticity and its relation to stability will be also addressed and the bridge to an axiomatic formulation of stochastic electrodynamics will be constructed.
Motivated by Hilbert's sixth problem on axiomatization of physics, the author is proposing a rather provocative abstract axiomatic framework called S - formalization, where S is an arbitrary physical system .The proposal is an attempt to provide a general axiomatic framework , from which mathematical frameworks of new physical theories can be formulated on firm axiomatic basis and the mathematical frameworks of subjects such as standard (nonrelativistic) quantum mechanics are naturally derived as special cases of this general axiomatic framework. Introduction