MAT-55216 Topics in Applied Mathematics, 3 credits

Fall 2012: Applied Stochastic Differential Equations

Teacher: Dr. Tech. Simo Särkkä, Aalto University, Finland

Coordinator: Prof. Robert Piché, Mathematics Dept, TUT

Schedule: Lectures & Exercises Thursdays 1-4pm (25.10, 1.11, 8.11., 15.11., 22.11.). The exercise hour is 1-2pm and the lecture is 2-4pm. Location: Tampere University of Technology room Td308 (bring a laptop with Matlab/Octave)

Topics: An introduction to the theory, applications and numerical methods for SDEs. Applications include biology, finance, computational statistics, communications engineering, fluid dynamics, and mechanical vibrations. After the course the student should be able to formulate a simple SDE model for an application, analyze its properties, and solve it numerically using appropriate methods.

Prerequisites: Multivariate differential and integral calculus, matrix analysis, basic probability, Matlab/Octave.

Course Pass Requirements:

  • The grade will be based on the project work. See Project work instructions and topics. (Deadlines: 30.11. and 31.12.)
  • Total 2/3 of the home work problems must be completed (see instructions below).


The slides are copied here after each lecture (the topics are preliminary and might change):

  1. Thursday 25.10. 2-4pm: Pragmatic Introduction to Stochastic Differential Equations (Slides as PDF)
  2. Thursday 1.11. 2-4pm: Ito Calculus and Stochastic Differential Equations (Slides as PDF)
  3. Thursday 8.11. 2-4pm: Probability Distributions and Statistics of SDEs (Slides as PDF)
  4. Thursday 15.11. 2-4pm: Numerical solutions of SDEs, Ito-Taylor Series, Gaussian Process Approximations (Slides as PDF)
  5. Thursday 22.11. 2-4pm: Further Topics; Series Expansions, Feynman-Kac, Girsanov Theorem, Filtering Theory (Slides as PDF)

Exercise hours:

Before each lecture there is an exercise hour, which works as follows: In the beginning, you should flag to a list which of the exercises you have completed. One person will be randomly selected to present his/her answer on the drawing board or computer. Note that in the end of the course you must have done and flagged total of 2/3 of all the exercises during the course (8 out of 12 exercises).

On the first day 25.10. 1-2pm there will be a voluntary introductory demonstration session on ordinary differential equations before the lecture starts at 2pm.

Attention: Below you can find a set of extra exercises which can be returned to reach the required amount of 8 points. You can get single point from each exercise and the answers should be returned to the lecturer in PDF/Matlab form by December 16th, 2012:

Project Work:

The grade of the course will be based on a project work. See Project work instructions and topics. (Deadlines: 30.11. and 31.12.)

Course Material:

The primary course material consists of a set of lecture notes and slides which are available here in PDF form. The lecture notes can be found below:

Students might find the following books useful as well:

  • Gardiner: Stochastic Methods: A Handbook for the Natural and Social Sciences, Springer.
  • Gardiner: Handbook of Stochastic Methods, Springer (old version of the above).
  • Oksendal: Stochastic Differential Equations, Springer.