2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/100089We discuss stochastic derivations, stochastic Hamiltonians and the flows that they generate, algebraic fluctuaion-dissipation theorems, etc., in a language common to both classical and quantum algebras. It is convenient to define distinct notions of time-ordered exponentials to take account of the breakdown of the Leibniz rule in the Ito calculus. We introduce a notion of quantum Stratonovich calculus and show how it relates to Stratonovich-Dyson time ordered exponentials. We then use it to demonstrate a natural way to add stochastic derivations.18 pages, no figures, updated with discussion on various notions of time-ordered exponentials (Ito/Stratonovich/exponentiated)and their distinct role in quantum stochastic limitsQuantum Physicstext