Stochastic Differential Equations and Ontology

This book challenges the classical view of stochastic processes as merely mathematical models of randomness and instead presents them as fundamental ontological components of nature. While deterministic thinking has long treated randomness as error or epistemic limitation, modern developments in Brownian motion, stochastic differential equations, Lévy processes, fractional Brownian motion, stochastic flows, and random geometry reveal randomness as an intrinsic feature of reality. By reinterpreting the mathematical foundations of these processes, the book develops a stochastic ontology that offers a unified conceptual framework for disciplines including physics, biology, economics, artificial intelligence, neuroscience, quantum technologies, and philosophy. Through the Wiener-Lévy-fBM perspective, continuity, discontinuity, and memory are shown to shape the stochastic structure of time and space, opening new interdisciplinary horizons.