Stochastic Processes with Physical Applications

Many physical systems in the real world do not behave deterministically; instead, they are driven by randomness, fluctuations, and noise. Understanding these systems requires a solid grasp of stochastic processes—the mathematical language of random evolution over time. This course equips you with the essential theoretical tools to model, analyze, and interpret random phenomena in physical systems. You will transition from basic probability concepts to physical models, gaining the confidence to apply stochastic methods to real-world scientific problems. What you'll learn: - Understand foundational probability theory, random variables, and the transition to stochastic processes. - Analyze random walks and their direct connection to physical diffusion processes. - Master Markov chains and continuous-time Markov processes to model system state transitions. - Apply the Langevin equation to describe Brownian motion and fluctuating forces. - Derive and solve the Fokker-Planck equation to track probability density evolution. - Explore modern concepts in stochastic thermodynamics and noise in physical measurements. You will begin by establishing core mathematical definitions and probability basics before diving into classic physical models of random motion. As you progress, you will read through detailed derivations, conceptual breakdowns, and written exercises that bridge mathematical theory with physical reality. This course is designed for undergraduate students, physics enthusiasts, and beginning researchers who want to understand random processes; no advanced background in measure theory is required as we start with foundational definitions and build up step-by-step. Start reading today to unlock the mathematical frameworks that govern the random nature of our universe.