Stochastic dynamics

Stochastic dynamics is the study of dynamical processes that occur on sufficiently large time scales such that the fast microscopic degrees of freedom can effectively be described as stochastic noise. The paradigmatic case is the diffusion of a Brownian particle in a fluid. Two fundamentally different yet equivalent differential equations describe this situation: the Fokker-Planck equation (a partial differential equation, PDE) and the Langevin equation (a stochastic differential equation, SDE, that requires stochastic calculus). For processes with jumps, one deals with a master equation. This lecture offers an introduction into all three types of equations. We also will cover many applications, including examples from biophysics and econophysics. A background in statistical physics is helpful but not required to attend this lecture.