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Durham University

Faculty Handbook Archive

Archive Module Description

This page is for the academic year 2021-22. The current handbook year is 2022-23

Department: Mathematical Sciences

MATH4091: STOCHASTIC PROCESSES IV

Type Open Level 4 Credits 20 Availability Available in 2021/22 Module Cap Location Durham

Prerequisites

  • Analysis in Many Variables II (MATH2031) AND Probability II (MATH2647)

Corequisites

  • None.

Excluded Combination of Modules

  • Stochastic Processes III (MATH3251).

Aims

  • This module continues on from the treatment of probability in Probability II (MATH2647).
  • It is designed to introduce mathematics students to the wide variety of models of systems in which sequences of events are governed by probabilistic laws.
  • Students completing this course should be equipped to read for themselves much of the vast literature on applications to problems in physics, engineering, chemistry, biology, medicine, psychology and many other fields.

Content

  • Probability revision.
  • Branching processes.
  • Coupling.
  • Martingales and applications.
  • Poisson processes.
  • Continuous-time Markov chains.
  • Brownian motion.
  • Additional topics in stochastic processes.

Learning Outcomes

Subject-specific Knowledge:
  • By the end of the module students will: be able to solve novel and/or complex problems in Stochastic Processes.
  • have a systematic and coherent understanding of theoretical mathematics in the field of Stochastic Processes.
  • have acquired coherent body of knowledge of these subjects demonstrated through one or more of the following topic areas:
  • Probability.
  • Discrete Parameter Martingales.
  • Brownian motion.
  • Poisson processes.
  • Continuous-time Markov processes.
  • Coupling.
Subject-specific Skills:
  • In addition students will have highly specialised and advanced mathematical skills in the following areas: Modelling, Computation.
Key Skills:
  • Students will be able to study independently to further their knowledge of an advanced topic.

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.
  • Subject material assigned for independent study develops the ability to acquire knowledge and understanding without dependence on lectures.
  • Assignments for self-study develop problem-solving skills and enable students to test and develop their knowledge and understanding.
  • Formatively assessed assignments provide practice in the application of logic and high level of rigour as well as feedback for the students and the lecturer on students' progress.
  • The end-of-year examination assesses the knowledge acquired and the ability to solve complex and specialised problems. The Subject material assigned for independent study will form part of the examined material.

Teaching Methods and Learning Hours

Activity Number Frequency Duration Total/Hours
Lectures 42 2 per week for 20 weeks and 2 in term 3 1 Hour 42
Problems Classes 8 Four in each of terms 1 and 2 1 Hour 8
Preparation and Reading 150
Total 200

Summative Assessment

Component: Examination Component Weighting: 100%
Element Length / duration Element Weighting Resit Opportunity
Written examination 3 Hours 100%

Formative Assessment:

Eight written assignments to be assessed and returned. Other assignments are set for self-study and complete solutions are made available to students.


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