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DEGREE REGULATIONS & PROGRAMMES OF STUDY 2021/2022

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DRPS : Course Catalogue : School of Mathematics : Mathematics

Postgraduate Course: Stochastic Modelling (MATH11029)

Course Outline
SchoolSchool of Mathematics CollegeCollege of Science and Engineering
Credit level (Normal year taken)SCQF Level 11 (Postgraduate) AvailabilityNot available to visiting students
SCQF Credits10 ECTS Credits5
SummarySyllabus 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.
Course description Not entered
Entry Requirements (not applicable to Visiting Students)
Pre-requisites Co-requisites
Prohibited Combinations Students MUST NOT also be taking Stochastic Modelling (MATH10007)
Other requirements None
Course Delivery Information
Academic year 2021/22, Not available to visiting students (SS1) Quota:  None
Course Start Semester 1
Timetable Timetable
Learning and Teaching activities (Further Info) Total Hours: 100 ( Lecture Hours 20, Seminar/Tutorial Hours 10, Summative Assessment Hours 2, Programme Level Learning and Teaching Hours 2, Directed Learning and Independent Learning Hours 66 )
Assessment (Further Info) Written Exam 80 %, Coursework 20 %, Practical Exam 0 %
Feedback Not entered
Exam Information
Exam Diet Paper Name Hours & Minutes
Main Exam Diet S1 (December)Stochastic Modelling (MATH11029)2:00
Learning Outcomes
On completion of this course, the student will be able to:
  1. Formulate mathematically a range of real-life scenario of a stochastic process described in words.
  2. Demonstrate an understanding of discrete and continuous time stochastic processes by being able to calculate finite dimensional distributions.
  3. Analyse the transient behaviour of Markov chains, and classify their states.
  4. Demonstrate an understanding of stationary and limiting behaviour by deriving corresponding probability distributions, and first passage properties.
  5. Calculate the finite dimensional distributions of Poisson processes.
Reading List
R. Durrett. Essentials of Stochastic Processes, Springer, 2012. V. Kulkarni. Modeling and Analysis of Stochastic Systems, CRC Press, 2010.
Additional Information
Course URL https://info.maths.ed.ac.uk/teaching.html
Graduate Attributes and Skills Not entered
KeywordsSM_OR
Contacts
Course organiserDr Theo Assiotis
Tel:
Email: theo.assiotis@ed.ac.uk
Course secretaryMiss Gemma Aitchison
Tel: (0131 6)50 9268
Email: Gemma.Aitchison@ed.ac.uk
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