Module MATH3251: STOCHASTIC PROCESSES III

Department: Mathematical Sciences

MATH3251: STOCHASTIC PROCESSES III

Prerequisites

• Analysis in Many Variables II (MATH2031), Markov Chains II (MATH2707) OR Probability II (MATH2647)

Corequisites

• None.

Excluded Combination of Modules

Aims

• To develop models for processes evolving randomly in time, and probabilistic methods for their analysis, building on the treatment of probability at Levels 1 and 2. Students completing this course should be equipped to read for themselves much of the vast literature on applications of stochastic processes to problems in physics, engineering, chemistry, biology, medicine, psychology, and other fields.

Content

• Branching processes
• Poisson processes
• Continuous-time Markov chains
• Discrete-time martingales and their applications
• Discrete renewal theory
• Further topics chosen from: coupling; further applications of martingale theory; general renewal theory; queueing theory

Learning Outcomes

• By the end of the module students will: be able to solve seen and unseen problems on the given topics.
• Have a knowledge and understanding of this subject demonstrated through an ability to compute probabilities of events associated with a variety of important stochastic processes, and to analyse the behaviour of such processes.
• Reproduce theoretical mathematics concerning stochastic processes at a level appropriate to Level 3, including key definitions and theorems.

• In addition students will have enhanced mathematical skills in the following areas: Modelling, Computation.

• Students will have basic mathematical skills in the following areas: problem solving, modelling, computation.

Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module

• Lectures demonstrate what is required to be learned and the application of the theory to practical examples.
• Problems classes show how to solve example problems in an ideal way, revealing also the thought processes behind such solutions.
• Formative assessments provide feedback to guide students in the correct development of their knowledge and skills in preparation for summative assessment.
• The end-of-year examination assesses the knowledge acquired and the ability to solve predictable and unpredictable problems.

Teaching Methods and Learning Hours

Summative Assessment

Formative Assessment:

Four assignments in each of the first two terms.

■ Attendance at all activities marked with this symbol will be monitored. Students who fail to attend these activities, or to complete the summative or formative assessment specified above, will be subject to the procedures defined in the University's General Regulation V, and may be required to leave the University