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Department of Mathematics & Statistics

STAT444 Stochastic Processes

Second Semester
20 points

Stochastic processes are intrinsic to many real world problems and also find application in a number of statistical techniques. This course introduces both the theory of stochastic processes and their use in modelling physical, biological and financial systems.

Paper details

An introduction to stochastic processes and stochastic calculus, emphasizing both theory and practical application.

Potential students

Any student interested in techniques that can be used to model many important physical, biological and financial processes. The only prerequisite is STAT 362.

Main topics

  • Random walks
  • Markov chains
  • Poisson processes
  • Birth and death processes
  • Queues
  • Branching processes
  • Gaussian processes
  • Itô calculus
  • Stochastic differential equations


STAT 362

Required text


Useful references

P.W. Jones & P. Smith (2001) Stochastic Processes: An Introduction, Arnold

D.R. Cox & H.D. Miller (1965) The theory of stochastic processes, Methuen

J. Michael Steele (2001) Stochastic Calculus and Financial Applications, Springer


Dr Matthew Parry, room 236, phone 479-7780


Tuesday 10-12pm (Rm 240).

Internal Assessment

The internal assessment comes from 8 assignments

Exam format

3-hour final exam with 6 questions

Final mark

Your final mark F in the paper will be calculated according to this formula:

F = max(E, (2E + A)/3)


  • E is the Exam mark
  • A is the Assignments mark

and all quantities are expressed as percentages.

Students must abide by the University’s Academic Integrity Policy

Academic endeavours at the University of Otago are built upon an essential commitment to academic integrity.

The two most common forms of academic misconduct are plagiarism and unauthorised collaboration.

Academic misconduct: Plagiarism

Plagiarism is defined as:

  • Copying or paraphrasing another person’s work and presenting it as your own.
  • Being party to someone else’s plagiarism by letting them copy your work or helping them to copy the work of someone else without acknowledgement.
  • Using your own work in another situation, such as for the assessment of a different paper or program, without indicating the source.
  • Plagiarism can be unintentional or intentional. Even if it is unintentional, it is still considered to be plagiarism.

All students have a responsibility to be aware of acceptable academic practice in relation to the use of material prepared by others and are expected to take all steps reasonably necessary to ensure no breach of acceptable academic practice occurs. You should also be aware that plagiarism is easy to detect and the University has policies in place to deal with it.

Academic misconduct: Unauthorised Collaboration

Unauthorised Collaboration occurs when you work with, or share work with, others on an assessment which is designed as a task for individuals and in which individual answers are required. This form does not include assessment tasks where students are required or permitted to present their results as collaborative work. Nor does it preclude collaborative effort in research or study for assignments, tests or examinations; but unless it is explicitly stated otherwise, each student’s answers should be in their own words. If you are not sure if collaboration is allowed, check with your lecturer.

Further information

While we strive to keep details as accurate and up-to-date as possible, information given here should be regarded as provisional. Individual lecturers will confirm teaching and assessment methods.
An epidemic can be modelled as a Markov process in which system states specify the compartment (susceptible, infectious, symptomatic, etc) of each member of the population. Although data on the spread of disease are typically highly incomplete, (Bayesian) inference is made tractable by the use of Markov chain Monte Carlo techniques.
The Russian mathematician (1856-1922) best known for his work in probability and for stochastic processes especially Markov chains.