Reading List

Lecture notes will be provided, but there are also many textbooks which cover the course material with a varying degrees of detail/rigour.
These include:

1. D. Revuz and M. Yor, Continuous martingales and Brownian motion, Springer (Revised \(3^{rd}\) ed.), 2001, Chapters 0-4.
2. I. Karatzas and S. Shreve, Brownian motion and stochastic calculus, Springer (\(2^{nd}\) ed.), 1991, Chapters 1-3.
3. R. Durrett, Stochastic Calculus: A practical introduction, CRC Press, 1996. Sections 1.1 - 2.10.
4. F. Klebaner, Introduction to Stochastic Calculus with Applications, 3rd edition, Imperial College Press, 2012. Chapters 1, 2, 3.1--3.11, 4.1-4.5, 7.1-7.8, 8.1-8.7.
5. J. M. Steele, Stochastic Calculus and Financial Applications, Springer, 2010. Chapters 3 - 8.
6. B. Oksendal, Stochastic Differential Equations: An introduction with applications, 6th edition, Springer (Universitext), 2007. Chapters 1 - 3.
7. S. Shreve, Stochastic calculus for finance, Vol 2: Continuous-time models, Springer Finance, Springer-Verlag, New York, 2004. Chapters 3 - 4.