The short-course starts
with basic background on stochastic differential equations
theory and numerics, including the Basics below.
The focus of the course is on explaining stochastic differential
equations on macro scales for phase transformation from
models on micro scales.

Basics (two times 45 minutes):

- definition of Brownian motion,
- Ito integrals, Ito SDEs as forward Euler (and Stratonovich as trapezoidal),
- Kolmogorov's equations, weak and strong approximation,

Micro to macro applications (4 times 45 minutes):

- Ehrenfest and Born-Oppenheimer dynamics explained from the Schrödinger equation,
- Smoluchowski and Langevin dynamics,
- Macroscopic stochastic phase-field explained from Smoluchowski molecular dynamics

Course material:

lecture notes

slides 1

slides 2

slides 3

draft

Teacher: Anders Szepessy

Welcome

Anders Szepessy,

szepessy@kth.se, 790 7494