Ontology of Stochastic Differential Equations

Abstract

This study provides a comprehensive examination of the mathematical formulations, ontological foundations, and application domains of stochastic differential equations (SDEs). SDEs play a critical role in modeling complex phenomena such as uncertainty and randomness and can be applied across a wide range of fields from financial markets to biological systems. The paper contrasts the mathematical approaches of Itô and Stratonovich calculus, detailing the solution methods and theoretical foundations of SDEs. Additionally, the ontological foundations of SDEs and their applications in various scientific and engineering fields are explored. Emphasis is placed on their use in finance, biology, cryptology, and blockchain technology. The results highlight the significance of SDEs in mathematical modeling and their impact across numerous application areas.