Postgraduate Course: Stochastic Modelling (MATH11029)
|School||School of Mathematics
||College||College of Science and Engineering
|Credit level (Normal year taken)||SCQF Level 11 (Postgraduate)
||Availability||Not available to visiting students
|Summary||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.
Entry Requirements (not applicable to Visiting Students)
|Prohibited Combinations|| Students MUST NOT also be taking
Stochastic Modelling (MATH10007)
||Other requirements|| None
Course Delivery Information
|Academic year 2023/24, Not available to visiting students (SS1)
|Course Start Date
|Learning and Teaching activities (Further Info)
Lecture Hours 20,
Seminar/Tutorial Hours 10,
Summative Assessment Hours 2,
Programme Level Learning and Teaching Hours 2,
Directed Learning and Independent Learning Hours
|Assessment (Further Info)
||Hours & Minutes
|Main Exam Diet S1 (December)||Stochastic Modelling (MATH11029)||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.
|R. Durrett. Essentials of Stochastic Processes, Springer, 2012. V. Kulkarni. Modeling and Analysis of Stochastic Systems, CRC Press, 2010.|
|Course organiser||Dr Theo Assiotis
|Course secretary||Miss Gemma Aitchison
Tel: (0131 6)50 9268