Stochastic Processes in Applied Physics: From Brownian Motion to Financial Modeling

Abstract

Stochastic processes are mathematical models used to describe systems that evolve over time with inherent randomness. This paper explores the application of stochastic processes in applied physics, focusing on their use in modeling phenomena such as Brownian motion and financial systems. The study begins with a foundational overview of stochastic processes, detailing their mathematical framework and key concepts. It then transitions to specific applications, including classical examples from statistical mechanics and modern applications in financial modeling. By examining the methodologies and results of various studies, this paper aims to highlight the versatility and significance of stochastic processes in understanding and predicting complex systems in physics and finance.