# DEGREE REGULATIONS & PROGRAMMES OF STUDY 2023/2024

### Timetable information in the Course Catalogue may be subject to change.

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# 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 SCQF Credits 10 ECTS Credits 5 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. 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.
 Pre-requisites Students MUST have passed: Several Variable Calculus and Differential Equations (MATH08063) AND Fundamentals of Pure Mathematics (MATH08064) AND Probability (MATH08066) Co-requisites Prohibited Combinations Students MUST NOT also be taking Stochastic Modelling (MATH11029) Other requirements Students can have passed Several Variable Calculus and Differential Equations (MATH08063) AND Fundamentals of Pure Mathematics (MATH08064) AND Probability with Applications (MATH08067)
 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? Yes
 Academic year 2023/24, Available to all students (SV1) Quota:  None Course Start Semester 1 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 S1 (December) Stochastic Modelling (MATH10007) 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 wordsDemonstrate 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 URL https://info.maths.ed.ac.uk/teaching.html Graduate Attributes and Skills Not entered Keywords SMo
 Course organiser Dr Theo Assiotis Tel: Email: theo.assiotis@ed.ac.uk Course secretary Miss Greta Mazelyte Tel: Email: greta.mazelyte@ed.ac.uk
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