Undergraduate Course: Stochastic Modelling (MATH10007)
|School||School of Mathematics
||College||College of Science and Engineering
|Credit level (Normal year taken)||SCQF Level 10 (Year 3 Undergraduate)
||Availability||Available to all students
|Summary||This is an advanced probability course dealing with discrete and continuous time Markov chains. The course covers the fundamental theory, and provides many examples. Markov chains has countless applications in many fields raging from finance, operation research and optimization to biology, chemistry and physics.
Markov Chains in discrete time: classification of states, first passage and recurrence times, absorption problems, stationary and limiting distributions.
Markov Processes in continuous time: Poisson processes, birth-death processes.
The Q matrix, forward and backward differential equations, imbedded Markov Chain, stationary distribution.
Syllabus summary: Probability review: Conditional probability, basic definition of stochastic processes. Discrete-time Markov chains: Modelling of real life systems as Markov chains, transient behaviour, limiting behaviour and classification of states, first passage and recurrence times, absorption problems, ergodic theorems, Markov chains with costs and rewards, reversibility. Poisson processes: Exponential distribution, counting processes, alternative definitions of Poisson processes, splitting, superposition and uniform order statistics properties, non-homogeneous Poisson processes. Continuous-time Markov chains: transient behaviour, limiting behaviour and classification of states in continuous time, ergodicity, basic queueing models.
Information for Visiting Students
|Pre-requisites||Visiting students are advised to check that they have studied the material covered in the syllabus of each prerequisite course before enrolling.
|High Demand Course?
Course Delivery Information
|Academic year 2022/23, Available to all students (SV1)
|Learning and Teaching activities (Further Info)
Lecture Hours 22,
Seminar/Tutorial Hours 5,
Summative Assessment Hours 2,
Programme Level Learning and Teaching Hours 2,
Directed Learning and Independent Learning Hours
|Assessment (Further Info)
|Additional Information (Assessment)
||Coursework 5%, Examination 95%
||Hours & Minutes
|Main Exam Diet S1 (December)||2:00|
On completion of this course, the student will be able to:
- Formulate mathematically a range of real-life scenario of a stochastic process described in words
- Demonstrate an understanding of discrete and continuous time stochastic processes by being able to calculate finite dimensional distributions.
- Analyse the transient behaviour of Markov chains, and classify their states.
- Demonstrate an understanding of stationary and limiting behaviour by deriving corresponding probability distributions, and first passage properties.
- Calculate the finite dimensional distributions of Poisson processes.
|1. R. Durrett. Essentials of Stochastic Processes, Springer, 2012. |
2. V. Kulkarni. Modeling and Analysis of Stochastic Systems, CRC Press, 2010.
|Course organiser||Dr Theo Assiotis
|Course secretary||Miss Greta Mazelyte