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MAS3917 : Stochastic Processes

  • Offered for Year: 2024/25
  • Module Leader(s): Professor Hongsheng Dai
  • Owning School: Mathematics, Statistics and Physics
  • Teaching Location: Newcastle City Campus

Your programme is made up of credits, the total differs on programme to programme.

Semester 1 Credit Value: 10
ECTS Credits: 5.0
European Credit Transfer System


To introduce a number of mathematical models that account for stochastic (random) variations that are often necessary to model real world phenomena. Key concepts of stochastic processes will be explored in various settings.

Module summary

When modelling real world systems through time, we may wish to model the uncertainty inherent in the system. Such models require an appropriate collection of random variables indexed through time. We will illustrate how stochastic processes can help us understand complex dynamical systems.

The first part of the module will involve a review of probability theory, particularly conditional probability. We will then introduce random walks and Markov chains. Birth-death models and queuing systems will also be explored.

Outline Of Syllabus

Review of probability ideas: for instance, conditioning arguments. Gambling problems. Random walks. Markov chains: definition and examples, Chapman Kolmogorov equations, classification of states, notions of transience and recurrence, stationary distributions, simulation. Advanced topics may include: queueing, epidemic models.

Teaching Methods

Teaching Activities
Category Activity Number Length Student Hours Comment
Guided Independent StudyAssessment preparation and completion151:0015:00Completion of in course assessments
Scheduled Learning And Teaching ActivitiesLecture51:005:00Problem Classes
Scheduled Learning And Teaching ActivitiesLecture21:002:00Revision Lectures
Scheduled Learning And Teaching ActivitiesLecture201:0020:00Formal Lectures
Guided Independent StudyIndependent study581:0058:00Preparation time for lectures, background reading, coursework review
Teaching Rationale And Relationship

Teaching methods are appropriate to allow students to develop a wide range of skills, from understanding basic concepts and facts to higher-order thinking. Lectures are used for the delivery of theory and explanation of methods, illustrated with examples, and for giving general feedback on marked work. Problem classes are used to help develop the students’ abilities at applying the theory to solving problems

Assessment Methods

The format of resits will be determined by the Board of Examiners

Description Length Semester When Set Percentage Comment
Written Examination1201A80N/A
Other Assessment
Description Semester When Set Percentage Comment
Prob solv exercises1M5Problem-solving exercises assessment
Prob solv exercises1M5Problem-solving exercises assessment
Prob solv exercises1M5Problem-solving exercises assessment
Prob solv exercises1M5Problem-solving exercises assessment
Assessment Rationale And Relationship

A substantial formal unseen examination is appropriate for the assessment of the material in this module. The format of the examination will enable students to reliably demonstrate their own knowledge, understanding and application of learning outcomes. The assurance of academic integrity forms a necessary part of the programme accreditation.

Exam problems may require a synthesis of concepts and strategies from different sections, while they may have more than one ways for solution. The examination time allows the students to test different strategies, work out examples and gather evidence for deciding on an effective strategy, while carefully articulating their ideas and explicitly citing the theory they are using.

The coursework assignments allow the students to develop their problem solving techniques, to practise the methods learnt in the module, to assess their progress and to receive feedback; these assessments have a secondary formative purpose as well as their primary summative purpose.

Reading Lists