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DRPS : Course Catalogue : School of Mathematics : Mathematics

Undergraduate Course: Stochastic Modelling (MATH10007)

Course Outline
SchoolSchool of Mathematics CollegeCollege of Science and Engineering
Credit level (Normal year taken)SCQF Level 10 (Year 3 Undergraduate) AvailabilityAvailable to all students
SCQF Credits10 ECTS Credits5
SummaryCore course for Honours Degrees involving Statistics; optional course for Honours degrees involving Mathematics. 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.
Course description 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.
Entry Requirements (not applicable to Visiting Students)
Pre-requisites Students MUST have passed: Several Variable Calculus and Differential Equations (MATH08063) AND Fundamentals of Pure Mathematics (MATH08064) AND ( Probability (MATH08066) OR Probability with Applications (MATH08067))
Prohibited Combinations Other requirements None
Information for Visiting Students
High Demand Course? Yes
Course Delivery Information
Academic year 2015/16, Available to all students (SV1) Quota:  None
Course Start Semester 2
Timetable Timetable
Learning and Teaching activities (Further Info) Total Hours: 100 ( Lecture Hours 22, Seminar/Tutorial Hours 5, Summative Assessment Hours 2, Programme Level Learning and Teaching Hours 2, Directed Learning and Independent Learning Hours 69 )
Assessment (Further Info) Written Exam 95 %, Coursework 5 %, Practical Exam 0 %
Additional Information (Assessment) Coursework 5%, Examination 95%
Feedback Not entered
Exam Information
Exam Diet Paper Name Hours & Minutes
Main Exam Diet S2 (April/May)Stochastic Modelling (MATH10007)2:00
Learning Outcomes
On completion of this course, the student will be able to:
  1. Basic understanding of stochastic processes and their characterization
  2. Ability to analyze the transient behaviour of Markov chains, and classify their states
  3. Understanding stationary and limiting behaviour and deriving these probability distributions
  4. Ability to calculate the finite dimensional distributions of Poisson processes
  5. Appreciating the range of applications, together with a facility to model appropriate problems in terms of a stochastic process
Reading List
Additional Information
Course URL
Graduate Attributes and Skills Not entered
Study Abroad Not Applicable.
Course organiserDr Tibor Antal
Tel: (0131 6)51 7672
Course secretaryMr Thomas Robinson
Tel: (0131 6)50 4885
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