The theory of stochastic integration attempts to define what it means to integrate one stochastic process against another, when the processes involved may have rough paths, like those of a Brownian motion. Doing this allows us to develop a calculus for such processes, and to develop a theory of stochastic differential equations (SDEs), the random analogue of ODEs. The theory has found applications in all areas of mathematics, and laid the foundations for the discipline of mathematical finance.
We will follow Philip E. Protter's book Stochastic Integration and Differential Equations, which is a readable and formally self-contained account of the theory.
The group is being organised by Marion Hesse, Curdin Ott and Alex Watson, with the support of Andreas Kyprianou. Everybody is welcome to attend.
The course will run on Wednesdays, 10:15-12:05 in the Wolfson lecture theatre 4W 1.7. The first session ran on 9 February.
The organisers will present the first three lectures, and then members of the audience will take over to present the remaining content. We are still looking for volunteers for the remaining talks. A tentative schedule follows:
We can provide copies of sections of the book to those presenting.
If you would like to borrow or look at a copy of the course book at any time, please get in touch.
Properties of Conditional Expectation (from David Williams, Probability with Martingales).
Since the first chapter of the course book contains an introduction to the relevant material, there are no formal prerequisites besides a course in measure theoretic probability. However, a course in martingale theory, such as Bath's MA40058, would be very helpful. Please get in touch if you are unsure.
Please contact the organisers mailing list with any questions.