 # MATH3361 Stochastic Differential Equations: Theory, Applications, and Numerical Methods

MATH3361 is a Mathematics Level III course. See the course overview below.

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 1  every 2 years.

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

More information: Course outline (pdf)

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

#### Course Aims

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.

#### Course Description

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.