Department of Physics

10ΕΛΕ02 Stochastic Processes in Physics

Course webpage:  https://eclass.uoa.gr/courses/PHYS246

Course outline

Course content

• Introduction: Random variables, distributions, moments, moment generating function, Bayes theorem.
• Estimation theory: Hypothesis testing, estimation of random variables.
• Central limit theorem: Proof, Levy processes.
• Discrete random walks: Fundamental equation, Polya theorem, mean number of distinct sites visited.
• Diffusion equation: Properties, probability current, boundary conditions, first passage time calculation.
• Brownian motion. It Itô-Stratonovich stochastic differential equations.
• Fokker-Planck equation. Langevin equation.
• Classical Caldeira-Leggett model.
• Introduction to Brownian path integrals: Feynman-Kac formula (derivation, applications).