Stochastic processes with applications to biological systems
The course will follow the pedagogical format of CW Gardiner - Handbook of Stochastic Methods. Random variables. Important discrete and continuous distributions. Stochastic processes. The Markov description. Chapman-Kolmogorov equation. Analysis of Markov processes. Brownian motion. Applications to chemical kinetics and biophysical systems. Master equation. Langevin and Fokker-Planck representations. Simulating stochastic processes. Gillespie algorithm. First passage time problems.
Students should develop familiarity with stochastic descriptions. They should be able to write down the stochastic description of various systems of interest. They will be able to use basic tools from linear algebra to derive steady-state properties and some time-dependent features of such stochastic processes. They will be able to develop simulations of stochastic processes under various approximations. The focus is on broad understanding and applicability rather than deep technical results.