Stochastic Differential Equations: Theory, Applications and Numerical Methods (MATH3361)

MATH3361 is a Mathematics Level III course.

Units of credit: 6

Prerequisites: MATH2011 or MATH2111 or MATH2018 (DN) or MATH2019(DN) or MATH2069(DN) and MATH2801 or MATH2901 or MATH2089(DN) or MATH2099(DN)

Cycle of offering: Term 3 every 2 years.

Graduate attributes: The course will enhance your research, inquiry and analytical thinking abilities.

More information: Please refer to the Course outline for further information.

Important additional information as of 2023

UNSW Plagiarism Policy

The University requires all students to be aware of its policy on plagiarism.

For courses convened by the School of Mathematics and Statistics no assistance using generative AI software is allowed unless specifically referred to in the individual assessment tasks.

If its use is detected in the no assistance case, it will be regarded as serious academic misconduct and subject to the standard penalties, which may include 00FL, suspension and exclusion.

If you are currently enrolled in MATH3361, you can log into UNSW Moodle for this course.

This course gives an introduction to the theory of stochastic differential equations (SDEs), explains real-life applications, and introduces numerical methods to solve these equations. Stochastic differential equation models play a prominent role in a range of application areas, including biology, chemistry, epidemiology, mechanics, microelectronics, economics, and finance. With the ongoing development of powerful computers, there is a real need to solve these stochastic models. The corresponding SDEs generalise the ordinary deterministic differential equations (ODEs).

Similarly to (deterministic) ODEs, analytical solutions of SDEs are rare, and therefore, numerical approximations have to be developed.

Stochastic differential equation models play a prominent role in a range of application areas, including biology, chemistry, epidemiology, mechanics, microelectronics, economics, and finance. This course studies the theory and applications of stochastic differential equations, the design and implementation on computers of numerical methods for solving these practical mathematical equations. The course will start with a background knowledge of random variables, Brownian motion, Ornstein-Uhlenbeck process. Other topics studied include: stochastic integrals, the Euler-Maruyama method, Milstein's higher order method, stability and convergence.