Undergraduate Course: Applied Stochastic Differential Equations (MATH10097)
|School||School of Mathematics
||College||College of Science and Engineering
|Credit level (Normal year taken)||SCQF Level 10 (Year 4 Undergraduate)
||Availability||Available to all students
|Summary||Stochastic differential equations (SDEs) are used extensively in finance, industry and in sciences. This course provides an introduction to SDEs that discusses the fundamental concepts and properties of SDEs and presents strategies for their exact, approximate, and numerical solution. The first part of the course focuses on theoretical concepts, including the definition of Brownian motion and stochastic integrals, and on analytical techniques for the solution of SDEs; The second part centres on numerical methods for both strong and weak approximations of solutions and introduces widely used numerical schemes. The last part of the course concentrates on identifying the long time properties of solutions of SDEs.
Probability Theory and Random Variables
Stochastic Processes: Basic Definitions, Brownian motion, stationary processes, Ornstein Uhlenbeck process, The Karhunen-Loeve expansion.
Markov and diffusion processes: Chapman-Kolmogorov equations, generator of a Markov Process and its adjoint, ergodic and stationary Markov processes, Fokker Planck Equation, connection between diffusion processes and SDEs.
Elements of Numerical Analysis of SDEs.
Information for Visiting Students
Course Delivery Information
|Not being delivered|
On completion of this course, the student will be able to:
- define Brownian motion and stochastic integral.
- manipulate and solve simple SDEs.
- write numerical algorithms in MATLAB for the solution of SDEs based on the Euler and Milstein's methods.
- identify long time properties of Markov processes.
|G.A. Pavliotis, Stochastic Processes and Applications, Springer (2014) (recommended)|
L C Evans, An introduction to stochastic differential equations, AMS (2013) (reference)
P E Kloeden & E Platen, Numerical solutions of stochastic differential equations, Springer (1999) (reference)
|Graduate Attributes and Skills
||Students not on the MSc in Computational Applied Mathematics programme MUST have passed (Probability MATH08066 or Probability with Applications MATH08067) and Honours Differential Equations MATH10066.
|Course organiser||Dr Kostas Zygalakis
Tel: (0131 6)50 5975
|Course secretary||Mrs Alison Fairgrieve
Tel: (0131 6)50 5045