MA8109 Stochastic processes and differential equations
Fall 2021
Messages
|| Date | Title | Message |
|---|---|---|
| 24.11 | Exam | More information, including possible main topics for the exam is now posted on the exam. Please read everything carefully. |
| 12.11 | Exam | Some more information about the exam, including who is going to take it when, is given at the page the exam. |
| 29.10 | Exam | The oral exam will take place Friday 03.12 and Tuesday 14.12. |
| 29.10 | Num. SDEs | All notes from the lectures on numerical SDEs are collected in one note, which can be found under Books and reading material below. Send me an email if (or when) you find some mistakes. |
| 18.10 | Exercises | Exercises for ch 4 and 5 in BØ (with solutions) are now available. |
| 14.08 | Lecture notes | The lecture notes from today's lecture is available here. |
| 14.08 | Project work | Send me your choice of project no later than October 20. More on the project can be found under the project. |
| 08.10 | Linear SDEs | Her is a note on linear SDEs from todays lecture. |
| 07.10 | Cancelling | Todays lecture is cancelled. The lecture tomorrow will only be digital (Zoom link on Blackboard). |
| 03.09 | Exercises | The first exercise is available |
| 02.09 | Lecture rooms | The lecture rooms have been switched: The correct ones are Thursday in R4, Friday in B2. |
| 23.08 | First lecture | Friday 08:15-10:00 in Realfagsbygget: R4. |
| 29.06. | Info meeting | Monday August 23th, 14:15-15:00, at room 734 SB2. - Info about the course. - Decide on times for the lectures. - Set up email list for the course. Cannot attend, but want to take the course? - Send an email to anne [dot] kvarno [at] ntnu [dot] no where you include the times you are not free (have other lectures). |
Welcome to MA8109 !
This PhD course is given every second year, and usually 4th and 5th year (Master) students take it along with PhD students.
What is this course about?
- Differential equations with noisy/uncertain coefficients (stochastic differential equations), and their solutions, continuous time stochastic processes: We give a mathematical background, the main results, some applications, including some simulation strategies.
Of the multitude of applications in science, engineering and other disciplines, the most famous one is perhaps the Black-Scholes model for option pricing in finance.
Who can take this course?
- Interested students at Master or PhD level.
- The level should be suitable for good 4th year students in the industrial mathematics program.
- It can be taken as a regular course (MA8109) or a 'fordypningsemne' (TMA4505).
- Hopefully, the lectures will be given on campus. It will however be possible for students not present in Trondheim to follow the course.
General information
Lecturer
- Office: 1348, SBII
- Office hours: TBA
Lectures:
- Thursday 14:15-16:00 in Realfagsbygget, R4
- Friday 08:15-10:00 in Berg, B2
The first regular lecture will be given Friday 27.08.
Project:
- To take the exam, you must prepare a small report about a topic related to stochastic differential equations not covered in the lectures.
- The project counts for 20% of the final grade.
Books and reading material
Main textbook
- Øksendal: Stochastic Differential Equations, Springer Verlag.
Available on Springer Link: https://link.springer.com/book/10.1007/978-3-642-14394-6 - Chapter 5.2 from the 5th edition.
Notes by Anne Kværnø
Notes by Harald Krogstad
Supplementary reading
- Easy introduction:
- T. Mikosch: Elementary Stochastic Calculus with Finance in View, World Scientific, 1998.
- Intermediate level:
- L. C. Evans: An Introduction to Stochastic Differential Equations, 2013, AMS (a very readable lecture note)
- J. Jacod and P. Protter: Probability Essentials, 2004, Spinger.
- R. Schilling and L. Partzsch: Brownian Motion, 2012, De Gruyter.
- H.-H. Kuo: Introduction to Stochastic Integration,2006, Springer.
- Advanced level:
- D. Revuz and M. Yor: Continuous Martingales and Brownian Motion, 2005, Springer.
- I. Karatzas and S. E. Shreve: Brownian Motion and Stochastic Calculus, 1991, Springer.
- Numerical solution of SDEs:
- P. E. Kloden and E. Platen: Numerical Solution of Stochastic Differential Equations, 1992, Springer
- G.N. Milstein, M.V. Tretyakov: Stochastic Numerics for Mathematical Physics, 2010, Springer.
Topics:
(Subject to minor modifications)
- Probability and measure theory (background)
- Independence and conditional expectation (main theorems)
- Brownian motion
- Martingale theory
- The Itô integral
- Itô calculus
- Stochastic differential equations
- Diffusions
- Numerical schemes for SDEs