Notebooks, exercises and scripts used in teaching FY8503 Advanced theoretical physics at NTNU in the autumn of 2023. The topic of the course is transport modelling with stochastic differential equation. The approach is quite applied, with a focus on numerical methods. The lecture notes are in the form of Jupyter Notebooks with numerous small examples that hopefully serve to illustrate the course content.
Other than the lecture notes, the main source will be Numerical Solution of Stochastic Differential Equations, by Kloeden and Platen. Available through SpringerLink when you are on campus or VPN: https://link.springer.com/book/10.1007/978-3-662-12616-5
We will also use some papers in the later lectures, I will keep the list up to date as we go along.
Below is a list of books that you may or may not find useful to look at. Personally, I find that the field of stocastic processes and differential equations is often somewhat dense with new notation and jargon, and I find it useful to look up the same topic in different books, as they often provide different perspectives or approaches to the same material.
This is a commonly used and widely cited textbook in the field, but with a quite theoretical/rigorous approach. Available from SpringerLink: https://link.springer.com/book/10.1007/978-3-642-14394-6
https://global.oup.com/academic/product/simple-brownian-diffusion-9780199664504
https://global.oup.com/academic/product/first-steps-in-random-walks-9780198754091
https://link.springer.com/book/10.1007/978-1-4471-0533-6
Chandrashekhar, S., "Stochastic Problems in Physics and Astronomy", Reviews of Modern Physics vol. 15, no. 1, pp. 1--89, 1943.
https://doi.org/10.1103/RevModPhys.15.1 https://facultystaff.richmond.edu/~olipan/Chandrashekhar.pdf