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Module Code - Title:

MS4217 - STOCHASTIC PROCESSES

Year Last Offered:

2025/6

Hours Per Week:

Lecture

2

Lab

2

Tutorial

0

Other

2

Private

3

Credits

6

Grading Type:

N

Prerequisite Modules:

MS4213

Rationale and Purpose of the Module:

The purpose of this module is introduce the students to the mathematical statistical analysis of probabilistic processes which develop over time.

Syllabus:

1. Recap on probability ( copies, expectation, MGF, PGF) 2. Random Walks (differences equations & their solutions) 3.Markov Chains (discrete state space, discrete time) 4. Markov Processes (discrete state space, continuous time) 5. Queues (multi-sever queues, steady state solutions) 6. Survival Analysis ( basic objects, covariates, MLE)

Learning Outcomes:

Cognitive (Knowledge, Understanding, Application, Analysis, Evaluation, Synthesis)

1. Identify an appropriate model for real world process from a description 2. Discuss the key mathematical assumptions underpinning the model 3. Set-up the resulting mathematical equations for the process 4. Recognise the correct method of solution 5. Solve the system of equations for the MGF or PGF 6. Utilise the MGF or PGF to deduce properties of the process.

Affective (Attitudes and Values)

1. Justify the choice of model for the process 2. Discuss the limitations of the underpinning mathematical assumptions 3. Suggest cogent modifcations which may improve the model 4. Display a professional attitude to statistical model development

Psychomotor (Physical Skills)

1. Demonstrate the solution to problems on the black or white board 2. Deliver technical explanations to the class

How the Module will be Taught and what will be the Learning Experiences of the Students:

1. By chalk and talk. 2. By projected PDF notes 3. By Tutorials 4. By wriitten course notes 5. By CA (20% ) homeworks 6. Students will learn enough theory to construct and analyse the class of stochastic processes covered on the syllabus

Research Findings Incorporated in to the Syllabus (If Relevant):

Where appropriate these are included as homework questions.

Prime Texts:

Jones & Smith (2001) Stoshatic Processes an Introduction , Arnold, London

Other Relevant Texts:

Cox & Miller (1970) The theory of Stochastic Processes , Methuen, London

Programme(s) in which this Module is Offered:

Semester(s) Module is Offered:

Module Leader:

david.osullivan@ul.ie