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Course syllabus - Introduction to Stochastic Processes

Scope

7.5 credits

Course code

MAA320

Valid from

Autumn semester 2025

Education level

First cycle

Progressive Specialisation

G2F (First cycle, has at least 60 credits in first-cycle course/s as entry requirements)

Main area(s)

Mathematics/Applied Mathematics

Organisation

School of Education, Culture and Communication

Ratified

2018-12-07

Revised

2024-12-10

Literature lists

Course literature is preliminary up to 8 weeks before course start. Course literature can be valid over several semesters.

    • Ratified date: 2025-05-09
    • Latest update: 2025-05-27

    Books

    Sheldon M. Ross,

    Introduction to Probability Models (Eleventh Edition)

    LIBRIS-ID: 16527673

    Academic Press,

    Other Materials

    Additional lecture notes will be used in the course.

Objectives

The course aims to give the student the opportunity to acquire basic knowledge in the area of stochastic processes.

Learning outcomes

At the end of the course the student is expected to be able to:

  1. compute probabilities, expectations, and variances by conditioning.
  2. classify states of discrete time Markov chains, calculate their long-run probabilities and mean time spent in transient states, apply Markov chain Monte Carlo methods for statistical simulation.
  3. explain properties of homogeneous, non-homogeneous and compound Poisson processes and apply them to real-life problems.
  4. derive the forward and backward differential equations for continuous time Markov chains, determine their long-run probabilities.
  5. explain properties of Brownian motions, such as stationary and independent increments, nowhere differentiability, hitting times.
  6. perform basic calculations for Gaussian and stationary processes, such as computing the autocorrelation function and linear filtering.
  7. apply theoretical knowledge to engineering areas such as option pricing, renewal, queueing, and reliability theories.

Course content

  • Conditional probabilities and conditional expectations. Computing probabilities, expectations, and variances by conditioning.
  • Discrete time Markov chains. Chapman-Kolmogorov equations. Classification of states. Long-run probabilities.
  • Counting processes. The Poisson process and its generalizations. Interarrival and waiting time distributions.
  • Continuous time Markov chains. Birth and death processes. The forward and backward differential equations. Long-run probabilities.
  • Brownian motions. Application to pricing stock options. Gaussian and stationary processes.Applications to renewal, queueing, and reliability theories.

Specific requirements

At least totally 60 credits in the technical, natural sciences, business administration or economics areas including Probability, 7.5 credits, and Basic Calculus, continuation course, 7.5 credits, or the equivalent.

Examination

TEN1, Written examination, 4.5 credits, individual written examination concerning learning outcomes 1-6, grades Fail (U), Pass (G) or Pass with distinction (VG)
SEM1, Seminar, 3 credits, active participation concerning learning outcome 7, grades Fail (U) or Passed (G)

There may also be optional assignments that give bonus points for the examinations above. See more information in the study guide.

A student who has a certificate from MDU regarding disability study support, can request adaptions for the examination. It is the examiner who takes decisions on any adaptions, based on the certificate and other conditions.

Grade

Three-grade scale